Polydispersity of molecular weight

Polydispersity of molecular weights of heparin was recognized in early studies (reviewed in Refs. 9 and 183). However, the polyelectrolyte nature and heterogeneity of charge distribution have hampered accurate determinations of molecular-weight distribution. 

There is a large body of literature on phase diagrams for pseudo-binary and pseudo-ternary polymer systems (pseudo- is to indicate polydispersity of molecular weights) with solvents [Flory, 1953 ... 

Initial, with the slope Si = d In rj /dint, related to polydispersity of molecular weights, Mz/M , where and Mr, are the z- and number-average molecular weight, respectively [337]. 

Polymer melts are not molecularly homogeneous. Even in homopolymers, there is polydispersity of molecular weights, while with copolymers there is almost always a variation of comonomer content between different molecules. In homopolymers. 

For preparative purposes batch fractionation is often employed. Although fractional crystallization may be included in a list of batch fractionation methods, we shall consider only those methods based on the phase separation of polymer solutions fractional precipitation and coacervate extraction. The general principles for these methods were presented in the last section. In this section we shall develop these ideas more fully with the objective of obtaining a more narrow distribution of molecular weights from a polydisperse system. Note that the final product of fractionation still contains a distribution of chain lengths however, the ratio M /M is smaller than for the unfractionated sample. 

A potential drawback of all the routes discussed thus far is that there is little control over polydispersity and molecular weight of the resultant polymer. Ringopening metathesis polymerization (ROMP) is a living polymerization method and, in theory, affords materials with low polydispersities and predictable molecular weights. This methodology has been applied to the synthesis of polyacctylcne by Feast [23], and has recently been exploited in the synthesis of PPV. Bicyclic monomer 12 [24] and cyclophane 13 [25) afford well-defined precursor polymers which may be converted into PPV 1 by thermal elimination as described in Scheme 1-4. 

According to the concepts, given in the paper [7], a significant difference between the values of yield stress of equiconcentrated dispersions of mono- and polydisperse polymers and the effect of molecular weight of monodisperse polymers on the value of yield stress is connected with the specific adsorption on the surface of filler particles of shorter molecules, so that for polydisperse polymers (irrespective of their average molecular weight) this is the layer of the same molecules. At the same time, upon a transition to a number of monodisperse polymers, properties of the adsorption layer become different. 

The importance of polydispersity is an interesting clue that it may be possible to tailor the weak interactions between polymer brushes by controlled polydispersity, that is, designed mixtures of molecular weight. A mixture of two chain lengths in a flat tethered layer can be analyzed via the Alexander model since the extra chain length in the longer chains, like free chains, will not penetrate the denser, shorter brush. This is one aspect of the vertical segregation phenomenon discussed in the next section. 

Calibration refers to characterizing the residence time in the GPC as a function of molecular weight. Axial dispersion refers to the chromatogram being a spread curve even for a monodisperse sample. A polydisperse sample then is the result of a series of overlapping, unseen, spread curves. 

Herein are reported improved methods of molecular weight calibration where simultaneously, peak broadening parameters (a) are obtained through the use of multiple polydisperse molecular weight standards. There are two basic methods covered. The first and most reliable method employs the universal molecular weight calibration curve obtained using narrow MWD polystyrene standards. 

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