Molar mass, of polymers

Table 6.1 Experimental methods for determining different types of average relative molar mass of polymers...

For practical purposes, the colligative property that is most useful for measuring relative molar masses of polymers is osmotic pressure. As Table 6.2 shows, all other properties take such small values that their measurement is impractical. 

Table 6.5 Change in titre o/O.OlM NaOH needed to neutralise 50 mg of polyester with relative molar mass of polymer (after H. Batzer and E. Lohse, Introduction to Macromolecular Chemistry , 2nd Edn., John Wiley Sons, Chichester, 1979)...

L length of the pore (nm) m effective resistance to water flux Mp. molar mass of polymer (g mol i)... 

Number-average molar mass of polymer chains between two adjacent crosslinks or junction points in a polymer network. 

This short overview illustrates the large complexity of the SEC processes and explains the absence of a quantitative theory, which would a priori express dependence between pore size distribution of the column packing—determined for example by mercury porosimetry—and distribution constant K in Equation 16.4. Therefore SEC is not an absolute method. The SEC columns must be either calibrated or the molar mass of polymer species in the column effluent continuously monitored (Section 16.9.1). 

Osmometry is used to determine the molar masses of polymers and natural macromolecules osmosis helps to transport nutrients in plants reverse osmosis is used in water purification. 

The number-average molar mass of polymer chains is defined as Mn = (mass of reacted monomers)/[(l/2) of chain ends] (3.161)... 

An abundance of data on the limiting viscosity number of polymer solutions can be found in the literature. This is because this quantity is generally used for the determination of the molar mass of polymers. Often the molar mass is not calculated at all and the limiting viscosity number (lvn) is used to characterise the polymer. 

Molar mass of polymers may be established from appropriate physical measurements on very dilute solutions or, if circumstances permit, by chemical analysis for end groups. The former methods are applied with difficulty at molar mass below 5000 to 10000 where as the chemical methods generally are reliable only for molar mass below about 25000. Hence, neither physical nor chemical methods alone are sufficients in all situations, but physical methods are definitely indicated for the high molar mass polymers of general interest. 

All of the physical methods presently used for the determination of molar mass of polymers require the molecules contribute individually, i.e., additively, to the property being measured, contribution due to interactions between pairs (or... 

It is clear that the interpolation between the calibration lines cannot be applied to mixtures of polymers (polymer blends). If the calibration lines are different, different molar masses of the homopolymers will elute at the same volume. The universal calibration is also not capable of eliminating the errors which originate from the simultaneous elution of two polymer fractions with the same hydrodynamic volume, but different composition and molar mass. Ogawa [33] has shown by a simulation technique that the molar masses of polymers eluting at the elution volume Ve are given by the corresponding coefficients K and a in the Mark-Houwink equation. 

Molar mass of polymers can be deduced from intrinsic viscosity measurement through a Mark-Houwink cahbration curve. This approach can be apphed to supramolecular polymers if Mark-Houwink and Huggins parameters are known [191]. However, finding a suitable covalent model to estimate these coefficients is a difficult task. 

Based on a caUhration curve prepared by measuring the elution volume of a series monodispersed polymer standards with known molecular weights, the molecular weight of a polymer sample can then be determined. Based on this principle, GPC determines the distribntion of Af, while Af, Af, and Af can also be calcnlated nsing other data. As GPC only measures molar masses of polymers indirectly, some researchers regard this techniqne as senuquantitative [53]. GPC can be conpled with mnltidimensional polymer HPLC techniques to obtain the qnantitative molar mass of complex polymer systems [54]. 

The most serious problems encountered in achieving correct estimates of the molar masses of polymers from their MALDI-TOF spectra do have an instrumental origin. For the quantitative analysis of mass spectra of polymers, the number of charged adducts revealed by the MS detector must reflect the number of polymeric chains actually existing in the sample. This requires that the ionization yield of the various oligomer species present in polymers must be independent of chain size, and that the MALDI-TOF detector ought to show a constant response to ions as the mass of the oligomer increases. 

Since the development of soft ionization mass spectrometry [9], which allows to analyze large organic molecules without fragmentation, various polymer architectures were characterized by mass spectrometry. In principle, different parameters tailoring polymeric material properties such as molar mass (MJ, architecture (linear, branched, cyclic, star, etc.), monomer composition, degree of functionalization, end groups, and the presence of impurities or additives can be evaluated by mass spectrometry, however, with some limitations. The determination of molar masses of polymers by mass spectrometry is only possible for reasonable low dispersity polymeric architectures, which can be achieved by using controllable polymerization techniques such as anionic or... 

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