Chain architecture branch distribution

Iedema, P.D. and Hoefsloot, H.C.J. (2001) Synthesis of branched polymer architectures from molecular weight and branching distributions for radical polymerisation with long-chain branching, accounting for topology-controlled random scission. Macromol. Theor. Simul., 10, 855. 

LCB polymers can be formed by chemically linking preformed polymers (arm first or polymer first method) or by growing polymer chains from a multifunctional initiatior (core first method). In both cases living polymerization techniques are preferred because they provide better control over MW, MW distribution and the final branching architecture. However, highly selective coupling reactions e.g. with multifunctional isocyanates, or dicyclohexylcar-bodiimide (DCC) coupling, have also been successful. 

Freed et al. [42,43], among others [44,45] have performed RG perturbation calculations of conformational properties of star chains. The results are mainly valid for low functionality stars. A general conclusion of these calculations is that the EV dependence of the mean size can be expressed as the contribution of two terms. One of them contains much of the chain length dependence but does not depend on the polymer architecture. The other term changes with different architectures but varies weakly with EV. Kosmas et al. [5] have also performed similar perturbation calculations for combs with branching points of different functionalities (that they denoted as brushes). Ohno and Binder [46] also employed RG calculations to evaluate the form of the bead density and center-to-end distance distribution of stars in the bulk and adsorbed in a surface. These calculations are consistent with their scaling theory [27]. 

The architecture dependence is also demonstrated in Fig. 33 by the factors of several star macromolecules, flexible cychc chains. Randomly and hyper-branched materials show a more complex behavior because of the large width in the molar mass distribution. Table 5 gives the actual values. The plot of Fig. 33 shows nicely how for a large number of arms the factor for hard spheres is approached. 

A useful approach to detection in polymer HPLC presents the on-line hyphenation of different measurement principles. For example, an RI detector combined with a UV photometer produces valuable additional information on the composition of some copolymers. Further progress was brought with the triple detection RI plus LALS plus VISCO [313], which is especially suitable for branched macromolecules and the tetra detection UV plus RI plus LALS plus VISCO, which enables characterization of some complex polymer systems, exhibiting a distribution not only in their molar mass and architecture, but also in their chemical composition such as long chain branched copolymers. 

In addition to linear polyphosphazenes with one type of side group, as shown in 3.1, other molecular architectures have also been assembled. These include polyphosphazenes in which two or more different side groups, R1 and R2, are arrayed along the chain in random, regular, or block distributions (3.2-3.4). Other species exist with short phosphazene branches linked to phosphorus atoms in the main chain (3.5,3.6). Also available are macromolecules in which carbon or sulfur replace some of the phosphorus atoms in... 

Polyethylene and polystyrene are two of the most commercially important and ubiquitous polymers, primarily because of their commercial value. Since the early days of polymer research there has been considerable interest to produce copolymers from ethylene (E) and styrene (S) because of both academic and business interests. Depending on the nature and type of polymerization chemistry, a variety of different molecular architectures can be produced. In addition to the different monomer distributions (random, alternating or blocky nature), there are possibilities for chain branching and tacticity in the chain microstructure. These molecular architectures have a profound influence on the melt and solid-state morphology and hence on the processability and material properties of the copolymers. 

The main feature of polymers is their MMD, which is well known and understood today. However, several other properties in which the breadth of distribution are important and influence polymer behavior (see Figure 1) include physical, the classical chain-length distribution chemical, two or more comonomers are incorporated in different fractions topological, polymer architecture may differ (e.g., linear, branched, grafted, cyclic, star or comb-like, and dendritic) structural, comonomer placement may be random, block, alternating, and so on and functional, distribution of chain functions (e.g., all chain ends or only some carry specific groups). Other properties the polymers may disperse (tacticity and crystallite dimensions) are not of the same general interest or cannot be characterized by solution methods. 

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