Linear polymer, definition

Classification Synthetic linear polymer Definition Polymer of 1-vinyl-2-pyrrolidone monomers... 

Another definition, taking into account polymerization conversion, has been more recently proposed.192 Perfect dendrimers present only terminal- and dendritic-type units and therefore have DB = 1, while linear polymers have DB = 0. Linear units do not contribute to branching and can be considered as structural defects present in hyperbranched polymers but not in dendrimers. For most hyperbranched polymers, nuclear magnetic resonance (NMR) spectroscopy determinations lead to DB values close to 0.5, that is, close to the theoretical value for randomly branched polymers. Slow monomer addition193 194 or polycondensations with nonequal reactivity of functional groups195 have been reported to yield polymers with higher DBs (0.6-0.66 range). 

The chemical and physical properties of the polymers obtained by these alternate methods are identical, except insofar as they are affected by differences in molecular weight. In order to avoid the confusion which would result if classification of the products were to be based on the method of synthesis actually employed in each case, it has been proposed that the substance be referred to as a condensation polymer in such instances, irrespective of whether a condensation or an addition polymerization process was used in its preparation. The cyclic compound is after all a condensation product of one or more bifunctional compounds, and in this sense the linear polymer obtained from the cyclic intermediate can be regarded as the polymeric derivative of the bifunctional monomer(s). Furthermore, each of the polymers listed in Table III may be degraded to bifunctional monomers differing in composition from the structural unit, although such degradation of polyethylene oxide and the polythioether may be difficult. Apart from the demands of any particular definition, it is clearly desirable to include all of these substances among the condensation... 

This technique is based on the use of a linear polymer with pendant functional groups that can be activated to initiate the polymerization of a second monomer. Based on this definition, the linear precursor polymer can be considered as a multifunctional macromolecular initiator. The importance of the grafting from technique by cationic polymerization of the second monomer increased considerably with the advent of living cationic polymerization. The advantage is the virtual absence of homopolymer formation via chain transfer to monomer. 

Because of the one-step polymerization procedure, hyperbranched polymers often contain not only D and T but also L repeating units. This can be expressed by DB, which is an important structural parameter of hyperbranched polymers. DB is estimated as the sum of the D and T units divided by the sum of all the three structural units, that is, D, T and L [41]. By definition, a linear polymer has no dendritic units and its DB is zero, while a perfect dendrimer has no linear units and its DB is thus unity. Frey has pointed out that DB statistically approaches 0.5 in the case of polymerization of AB2 monomers, provided that all the functional groups possess the same reactivity [42]. The structures of the hb-PYs could be analyzed by spectroscopic methods such as NMR and FTIR. The DB value of the phosphorous-containing polymer hb-F21, for example, was estimated to be 53% from its 31P NMR chemical shifts (Chart 1). 

A generating set R of n linear polymer elements is defined (Equation 21), where n represents the number of different kinds of polymer chains required. Each polymer has an additive inverse which will be written Pi"1, P2"1, etc. By definition the inverses subtract, or take away. Rings also require a zero which adds nothing to a system and which, in the multiplicative sense, removes everything. 

For the purposes of this review, we restrict the definition of PIMs to organic polymers which have interconnected pore structures and which exhibit appreciable apparent inner surface areas by gas sorption analysis. PIMs can be linear polymers (Sect. 2.2.1) or networks (Sect. 2.2.2). While other network polymers may be microporous (e.g. Sect. 2.1 and 2.4), it is this porosity of the linear analogues that distinguishes PIMs. Again, the area of PIMs has been reviewed quite recently [41,42] so relatively brief details are given here. 

Starting from the definition just given, the fact is encountered that not only linear polymers, but globular also can cover a far greater field than that according to the colloidal dimensions. As this book is devoted to colloid science, we will confine ourselves therefore chiefly to macromolecules up to 10 A only in special cases some reference will be made to larger ones. 

In the case of perfect dendritic branching as found in a dendrimer, the DB equals 1, while for linear polymers the DB is 0. In the case of eqn [1], even fully linear polymers would possess a DB > 0 thus this definition for DB can only describe DB accurately for branched products with rather high DP , when the number of dendritic units approximates the number of the terminal units. For lower molecular weight materials a different equation was developed systematically by Hdlter et al ... 

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