Branching Ideal branched structures

This approximation is equivalent to assuming that the differences in internal densities and, consequently, in solvent draining, between a branched chain and the homologous linear chain, when included in their corresponding mean sizes, can describe both the friction coefficient and the viscosity. Besides these theoretical considerations, an empirical correlation in terms of a log-log fit of h vs f was employed by Roovers et al. [51]. Kurata and Fukatsu [48] and Ptitsyn [82] performed a more general Kirwood evaluation of the friction coefficient for different types of ideal branched molecules (uniform and randomly distributed stars, combs and random-branched structures). Their results for different structures are included within the limits l[Pg.60]

Branching of polyethylenes provides the second dimension, after molar mass, with which to control properties. Tables 3.2 and 3.3. Branching of polyethylenes is a complex topic in this review it will be treated starting with the ideal copolymer structures formed with the new metallocene catalysts. Branched polyethylenes (BPE) provide increased toughness though decreased modulus and strength compared with LPE. Branches are obtained by copolymerization with 1-alkenes, such as... 

An ideal dendrimer structure without defects features only branched units and end-groups, in addition to the core (Figure 1). The molecules are monodisperse, i.e., they all possess the same molecular weight While this perfect structure is not required for catalysis and recovery in principle, it enables the precise characterization of polymer-boimd catalyst precursors. M ALDl-TOF is a particularly useful technique. 

Dendrimers branch perfectly with star-like topologies whereas hyperbranched polymers have imperfectly branched structures. Dendritic polymers have numerous sites per molecule to couple to active species, making them ideal carriers for drug molecules or biomacromolecules [96]. 

All the quantities so far defined relate to ideal networks, i.e., continuous branched structures without free chain ends. In reality, the number of such free chain ends increases with decreasing primary chain molecular weight. The molar concentration MX niol/g of effective network chains can, according to P. J. Flory, be calculated from the molar concentration [MJ of all the chains present for M )q > (M ) ,... 

Cluster mass distribution for ideal branched structures... 

The term dendrimer derives from the Greek word dendro for tree, and this indicates their three-dimensional branched structure. The molecules have a regularly branched structure, as shown in Fig. 2.32. In this idealized structure, each monomer group is cormected to three others, except at the periphery, giving a structure described as a Cayley tree with functionality f = 3. It is possible to synthesize dendrimers with different core, branch and surface imits. Due to steric effects there is a limit on the number of generations that can be grown . The structure shown in Fig. 2.32 is a fourth generation dendrimer. 

Dendritic macromolecules would be ideal candidates for cross-linking agents (11). They have highly synunetrical, perfectly branched structure and multiple reactive sites placed in the interior and at the periphery of the macromolecules. The number (density) of the junctions and their chemical composition can be easily controlled by the generation of the dendrimer (i.e. the number of reactive groups therein) and the chemistry used in the construction. 

In the case of n-butene isomerization it was demonstrated (Figure 2) that the ideal micro-pore topology led to retardation of the C8 dimer intermediate and that the catalyst based on the ferrierite structure was close to optimal in this respect [1). For selective isodewaxing a one-dimensional pore structure which constrained the skeletal isomerization transition state and thereby minimized multiple branching such as the SAPO-11 structure was found to meet these criteria. Clearly, these are ideal systems in which to apply computational chemistry where the reactant and product molecules are relatively simple and the micro-porous structures are ordered and known in detail. 

This closure property is also inherent to a set of differential equations for arbitrary sequences Uk in macromolecules of linear copolymers as well as for analogous fragments in branched polymers. Hence, in principle, the kinetic method enables the determination of statistical characteristics of the chemical structure of noncyclic polymers, provided the Flory principle holds for all the chemical reactions involved in their synthesis. It is essential here that the Flory principle is meant not in its original version but in the extended one [2]. Hence under mathematical modeling the employment of the kinetic models of macro-molecular reactions where the violation of ideality is connected only with the short-range effects will not create new fundamental problems as compared with ideal models. 

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