Recent Advances in Simulation of Dendritic Polymers
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Introduction
Dendrimers and hyperbranched polymers represent a novel class of structurally controlled macromolecules 1 derived from a branches-upon-branches structural motif. Dendrimers are well defined, highly branched macromolecules that radiate from a central core and are synthesized through a stepwise, repetitive reaction2 sequence that guarantees complete shells for each generation, leading to polymers that are monodisperse. The synthetic procedures developed for dendrimer preparation permit nearly complete control over the crit-2 ical molecular design parameters, such as size, shape, surface/interior chemistry, flexibility, and topology.1' 2
divergent strategy (Tomalia and coworkers', ), Synthetic techniques proved effective include the Starburst 3 the convergent growth strategy (Frdchet and coworkers ), and the self-assembly strategy (Zimmerman and 4 coworkers ). These methods have proved effective in generating macromolecules with a unique combination
of properties.se, The geometric characterization of dendrimer structure has lagged this rapid progress in synthesis and 1 design. The problem is that these molecules possess an enormous number of energetically permissible conformations, and in solution there is rapid interchange between them. Thus diffraction techniques yield little structure information. Also a number of generations involve the same monomers, making it difficult to extract precise information about the local structure from infrared or NMR experiments. Thus the most 2 precise experimental data about overall structure comes from size exclusion chromatography (SEC)."' The sites has come from NMR relaxation main experimental data about the geometric character of particular 7 times for molecules able to partially penetrate into the dendrimer. A particular advantage of using theory is that the properties of new materials can be predicted in advance of experiments. This allows the system to be adjusted and refined (designed) so as to obtain the optimal properties before the arduous experimental task of synthesis and characterization. However, there are significant challenges in using theory to predict accurate properties for functional dendritic materials. For 3 instance, an amorphous polymer within 1 p would have tens of billion of atoms, much too large for standard classical molecular dynamics (MD) and enormously too large for quantum mechanics (QM). Consequently. we use the multi-scale computational (MSC) hierarchical strategy, see Figure 1. The idea here is to start with accurate first principles QM on small system (10s or 100s of atoms). Based on the QM results, we then find force fields (FF) to replace the electrons in terms of springs. Using the FF allows classical MD simulations with 1000s of atoms. With current methods and hardware, MD is practical up to -10 million atoms, but 10 million atoms of a polymer occupy a cube of only -50 nm on a side. To treat much larger systems, it is essential to average the atoms into collective units (segments, grains, pseudoatoms). This is the mesosca
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