Branched polymers molecular distribution

Two types of well defined branched polymers are acessible anionically star-shaped polymers and comb-like polymers87 88). Such macromolecules are used to investigate the effect of branching on the properties, 4n solution as well as in the the bulk. Starshaped macromolecules contain a known number of identical chains which are linked at one end to a central nodule. The size of the latter should be small with respect to the overall molecular dimensions. Comb-like polymers comprise a linear backbone of given length fitted with a known number of randomly distributed branches of well defined size. They are similar to graft copolymers, except that backbone and branches are of identical chemical nature and do not exhibit repulsions. 

As early as 1952, Flory [5, 6] pointed out that the polycondensation of AB -type monomers will result in soluble highly branched polymers and he calculated the molecular weight distribution (MWD) and its averages using a statistical derivation. Ill-defined branched polycondensates were reported even earlier [7,8]. In 1972, Baker et al. reported the polycondensation of polyhydrox-ymonocarboxylic acids, (OH)nR-COOH, where n is an integer from two to six [ 9]. In 1982, Kricheldorf et al. [ 10] pubhshed the cocondensation of AB and AB2 monomers to form branched polyesters. However, only after Kim and Webster published the synthesis of pure hyperbranched polyarylenes from an AB2 monomer in 1988 [11-13], this class of polymers became a topic of intensive research by many groups. A multitude of hyperbranched polymers synthesized via polycondensation of AB2 monomers have been reported, and many reviews have been published [1,2,14-16]. 

The molecular distributions for polymers formed by condensations involving polyfunctional units of the type R—A/ resemble those for the branched polymers mentioned above, except for the important modification introduced by the incidence of gelation. The generation of an infinite network commences abruptly at the gel point, and the a-mount of this gel component increases progressively with further condensation. Meanwhile, the larger, more complex, species of the sol are selectively combined with the gel fraction, with the result that the sol fraction decreases in average molecular complexity as well as in amount. It is important to observe that the distinction between soluble finite species on the one hand and infinite network on the other invariably is sharp and by no means arbitrary. 

The method outlined above for characterizing branched polymers will hereafter be referred to as the molecular weight and branching distribution (MWBD) method. In the following sections, its application to the long chain branching in polyvinyl acetate and high pressure low density polyethylene will be demonstrated. 

In the absence of any nonsize exclusion effects or branching effects, the concentration distribution within the chromatographic peak describes the polymer molecular weight distribution. The concentration distribution is deduced from the response of a suitable detector. Detectors which respond to physicochemical properties other than concentration may also be of use in GPC. Over the past 25 years, a variety of detectors have been developed. This section reviews detectors available to the chromatographer. The detectors used in GPC can be grouped as... 

Different types of LCB are distinguished. Star polymers are the simplest branched polymers because they have only one branch point. Regular star polymers have a branch point with a constant number (functionality,/) of arms and every arm has the same molecular weight. They are therefore monodisperse polymers. Star polymers may also have arms with a most probable distribution [5], Star polymers can also be polydisperse due to a variable functionality. Palm tree [6] or umbrella polymers [7] that contain a single arm with different molecular weight (MW) than the other arms are classified under the asymmetric star [8] polymers, see Figure 3.2. 

GPC calibration curves are established based on the radius of gyration of known-molecular-weight polymers, such as well characterized, narrow-molecular-weight distribution polystyrene. Branched polymers have a lower radius of gyration for their molar mass than the corresponding linear molecule. Thus, as branching increases the GPC numbers become less and less accurate and so should only be used for trends, and not exact calculations as some authors have done. 

Complex polymers are those having a Joint distribution of molecular properties. Branched polymers, copolymers and stereoregular polymers fall within this category. For example, branched polymers have a joint... 

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