Structural simulation, hyperbranched polymers

For a theoretical description of crosslinking and network structure, network formation theories can be applied. The results of simulation of the functionality and molecular weight distribution obtained by TBP, or by off-space or in-space simulations are taken as input information. Formulation of the basic pgf characteristic of TBP for crosslinking of a distribution of a hyperbranched polymer is shown as an illustration. The simplest case of a BAf monomer corresponding to equation (4) is considered ... 

Assuming that all B groups have the same reactivity, the chemical reaction giving rise to a branched molecule is identical to the reaction resulting in a linear polymer. Statistically this will eventually result in a hyperbranched polymer. However, dependent on the chemical structure of the monomer, steric effects might favor the growth of linear polymers. Computer simulations of of ABX-monomer condensation and AB -monomers co-condensed with B-functional... 

Theoretical description of dendritic structures is an active but difficult topic because the length between branched points is close to or even smaller than the Kuhn length, above which the segments can be thought of as if they are freely jointed with each other. Most modeling or simulation work has focused on the quasi-static and rheological properties of hyperbranched polymers and dendrimers in shear flow [240, 244, 255-263]. Limited amounts of data were published for dendrimers and hyperbranched polymers within elongational flow field. 

Collectively, preliminary results reveal that dendrimers and hyperbranched polymers are more shear stable than other linear, cyclic, weakly grafted, and star cousins because of their unique structures. These polymers may fulfill the industry requirements where highly mechanically stable additives are needed. However, more experiments and simulations are required to gain sufficient insights into their CST and mechanochemistry. 

Le, Tu. C., Todd, B. D., Daivis, P. J., and Uhlherr, A. Structural properties of hyperbranched polymers in the melt nnder shear via nonequihhrium molecular dynamics simulation. The Journal of Chemical Physics, 130,074901 (2009). 

In this book, we first briefly review the structure, properties, and application of dendritic macromolecules in various fields. Next, molecular simulation techniques in hyperbranched polymer and dendrimers is reviewed. Lastly, we will survey the most characteristic and important recent examples in molecular simulation of dendritic architectures. 

Chain stiffness and the effects of excluded volume became the dominating issue in the years between 1980 and the start of the new millennium. Percolation simulations indicated strong effects on the unperturbed polymer conformations due to excluded volume interactions [4]. With specially synthesized model substances (prepared by the Burchard group), the transition from mean-field to highly perturbed conformation was explored [5-17]. Studies in 1996 [8] on randomly branched, and in 2004 on hyperbranched polymers [8, 18-20], showed that the fractal conception could be quantitatively adjusted to the scattering behavior of linear and branched structures over the whole (/-domain and offered valuable insight into the structure in space [16]. 

Figure 11 shows that within the wide range of pressures the simulations give a constant average number of branches. The microstructure of the polymer, however, is strongly affected by the pressure. Examples of the polymer structures obtained from the simulations are shown in Fig. 11. The polymers obtained at high pressures are mostly linear with a large fraction of atoms located in the main chain, and with relatively short and mostly linear side-chains. With a decrease in pressure the hyperbranched structures are formed. Both, the pressure independence of the branching number and the pressure influence on the polymer topology are in agreement with experimental data for Pd-catalysts [16,18-21].

For the propylene polymerization catalyzed by the complexes 1-7 (Scheme 2) the simulations were performed [27] based on the calculated energetics of the elementary reactions [ 13c-d]. For system 6 of Scheme 2, the calculated average number of branches is 238 br./lOO C, which is slightly larger than the experimental value of 213 br./lOO C. However, the temperature and pressure dependence of the number of branches and the polymer microstructure are in-line with experimental observations [21] 1) an increase in polymerization temperature leads to a decrease in the number of branches 2) olefin pressure does not affect the branching number, but affects the topology, leading to hyperbranched structures at lowp. 

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