Multiscale Modeling and Simulation Methods with Applications to Dendritic Polymers

Dendrimers and hyperbranched polymers represent a novel class of structurally controlled macromolecules derived from a branches-upon-branches structural motif. The synthetic procedures developed for dendrimer preparation permit nearly complete control over the critical molecular design parameters, such as size, shape, surface/interior chemistry, flexibility, and topology. Dendrimers are well-defined, highly branched macromolecules that radiate from a central core and are synthesized through a stepwise, repetitive reaction sequence that guarantees complete shells for each generation, leading to polymers that are monodisperse. This property of dendrimers makes it particularly natural to coarsen interactions in order to simulate dynamic processes occurring at larger length and longer time scales. In this paper we describe methods to construct three dimensional molecular structures of dendrimers (Continuous Configuration Boltzmann Biased direct Monte Carlo, CCBB MC) and methods towards coarse graining dendrimer interactions (NEIMO and hierarchical NEIMO methods) and representation of solvent dendrimer interactions through continuum solvation theories, Poisson Boltzmann (PB) and Surface Generalized Born (SGB) methods. We will describe applications to PAMAM, Stimuli response hybrid star-dendrimer polymers, and supra molecular assemblies crystallizing to A15 colloidal structure or Pm6m liquid crystals. 1. INTRODUCTON Dendrimers and hyperbranched polymers represent a novel class of structurally controlled macromolecules derived from a branches-upon-branches structural motif [1, 2]. Dendrimers are well defined, highly branched macromolecules that radiate from a central core and are synthesized through a stepwise, repetitive reaction sequence that guarantees complete shells for each generation, leading to polymers that are monodisperse [3]. The synthetic procedures developed for dendrimer preparation permit nearly complete control over the critical molecular design parameters, such as size, shape, surface/interior chemistry, flexibility, and topology [1-3]. Synthetic techniques proved effective include the Starburst divergent strategy of Tomalia and coworkers [1,2], the convergent growth strategy of Frechet and coworkers [4-6], and the self-assembly strategy of Zimmerman and coworkers [7]. These methods have proved effective in generating macromolecules with a unique combination of properties [8-11]. The geometric characterization of dendrimer structure has lagged and hence retarded the rapid progress in synthesis and design. The problem is that dendrimers possess an enormous number of energetically permissible conformations, and in solution there is frequent interchange between them. The 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 precise experimental data about overall structure comes from size exclusion chromatography (SEC). The main experimental data about the geometric character of particular sites has come from NMR relaxation times for molecules that partially penetrate into the dendrimer [12]. 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 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 of functional dendritic materials. Below we describe some recent developments in the area of dendrimers and molecular modeling applications to a list of dendritic polymers: PAMAM, stimuli responsive polymers, and colloidal crystals of self assembled dendrimers. The paper is organized as follows: In Section 2, we briefly describe the Continuous Configurational Boltzmann Biased (CCBB) direct Monte Carlo method [13-14] used in building the 3-dimensional molecular representations of the dendrimers used in this study, then the NEIMO and hierarchical NEIMO strategy [15-17]. In Section 2.d we describe Poisson Boltzmann and Surface Generalized Born approach for accurate and efficient treatment of continuum solvation in molecular dynamics simulation of polymers. Finally, in section 3 we describe the molecular mechanics and molecular dynamics applications on various dendrimers utilizing these methods.. 2. METHODS 2.1. The CCBB Direct Monte Carlo Method for Dendrimers To predict the properties of polymers, it is necessary to determine an ensemble of conformations highly populated at the temperature and pressure of interest. An efficient method for predicting these conformations is by using Monte Carlo (MC) sampling. Continuous Configurational Boltzmann Biased (CCBB) MC is an improved method that was developed for this purpose [13-14]. We have taken advantage of this method to generate energetically preferable 3-dimensional molecular structures of various dendrimers. The continuous configurational Boltzmann biased (CCBB) direct Monte Carlo method is developed on the basis of independent rotational sampling (IRS) method. In the IRS method, torsional degrees of the polymer chains are sampled using a weighting function based on the Boltzmann factor of the torsion energy. The normalized torsion weighting function (TWF), W IRS, for IRS is defined as IRS IRS IRS z g W ) ( ) ( φ φ =