Polymer science polydispersity

It has been found for some systems, and may be true for all, that there is no transition directly from the isotropic to the nematic phase as the critical condition is attained. Instead, a narrow biphasic region is found in which isotropic and nematic phases co-exist. This behaviour was predicted by Flory 2), even although his initial calculations related to monodisperse polymers. It is accentuated by polydispersity (see Flory s review in Vol. 59 of Advances in Polymer Science), and indeed for a polydisperse polymer the nematic phase is found to contain polymer at a higher concentration and of a higher average molecular weight than the isotropic phase with which it is in equilibrium. 

Polymerizations as part of liquid-phase organic reactions are also influenced by mass and heat transfer and residence time distribuhon [37, 48]. This was first shown with largely heat-releasing radical polymerizations such as for butyl acrylate (evident already at dilute concentration) [49]. Here, a clear influence of microreactor operation on the polydispersity index was determined. Issues of mass transfer and residence time distribution in particular come into play when the soluhon becomes much more viscous during the reachon. Polymerizahons change viscosities by orders of magnitude when carried out at high concentration or even in the bulk. The heat released is then even more of an issue, since tremendous hot spots may arise locally and lead to thermal runaway, known in polymer science as the Norrish-Tromsdorff effect. 

A mass-average molecular mass, M , is derived in Fig. 1.26. It is proportional to the second moment. The above mixture of equal mole fractions of largely different molar masses yields a mass-average molar mass, M , of 990,198. This is a better representation of the molecules in the mixture than given by M . Since most applications in polymer science deal with effects that scale with molar mass or volume and not number of molecules, it is more important to know M than M . The second equation for M lists a more detailed expression. You may want to check all four equations for the one most suitable for a given calculation. Finally Fig. 1.26 introduces the term polydispersity, a measure of the disparity between the size of molecules in the mixture. 

The synthesis of polymers, with attendant aspects of the thermodynamics and kinetics of polymerization that occupy entire textbooks (62,63), is to a very significant extent beyond the coverage of this text. Indeed, organic polymer science is often taught as a mate course to physical polymer science. However, since the thermodynamics and kinetics of polymerization affect both the molecular weights and the polydispersity index obtained, the most salient features of these areas will be explored. Polymer synthesis itself was briefly discussed in Section 1.4. 

It is customary in polymer science to deal with polydisper-sity indices. The two most conunon are M IM and MIM. Ideal polymer reactions have well-defined ratios, which are often approached in real polymerization reactions. MJM is so frequently used in this context that it often simply referred to as the PDI, or polydispersity index. 

Miyakoshi, R., Yokoyama, A., and Yokozawa, T. (2008a) Development of catalyst-transfer condensation polymerization. Synthesis of 7t-conjugated polymers with controlled molecular weight and low polydispersity. Journal of Polymer Science Part A-Polymer Chemistry, 46,753-765. 

Weight average molecular weight, quoted by the manufacturer. Polymer Sciences Laboratories Inc., Amherst, MA. The polydispersity quoted by the manufacturer is quite low, ranging from 1.03 to 1.06 for these polymers. 

We conclude that at present there is no strong basis for adopting any particular correlation for the effect of polydispersity on tIq. The only well-documented deviation from Eq. 5.4 occurs when a substantial number of rmentangled molecules are present. On the other hand, it may be unwise to accept Eq. 5.4 as a fundamental principle of polymer science. 

Fig. 21. Conversion and composition of phases at equilibrium (coexistence curves) calculated for an initial volume fraction of modifier, 4>mo = 0.177 in a castor oil (CO)-modified DGEBA-EDA system (Reprinted from Polymer, 35, CC. Riccardi, J. Borrajo, RJJ. Williams, Thermodynamic analysjs of phase separatimt in rubber-modilied thermosetting polymers influence of the reactive polj ner polydispersity, 5541-5550 Copyright (1994), with laid permission from Butterworth-Heinemiann journals, Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK)...

Patten, T.E., et al. 1996. Polymers with very low polydispersities from atom transfer radical polymerization. Science 272 866. 

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