UNCORRECTED PROOFMultiscale modeling and simulation methods with applicationsto dendritic polymersTahir Cagin*, Guofeng Wang, Ryan Martin, Georgios Zamanakos, Nagarajan Vaidehi, DanielT. Mainz, William A. Goddard IIIDivision of Chemistry and Chemical Engineering, Materials and Process Simulation Center (139-74), California Institute of Technology,Pasadena, CA 91125, USAReceived 21 September 2000; revised 2 February 2001; accepted 2 February 2001AbstractDendrimers 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 criticalmolecular design parameters, such as size, shape, surface/interior chemistry, ¯exibility, and topology. Dendrimers are well de®ned, highlybranched macromolecules that radiate from a central core and are synthesized through a stepwise, repetitive reaction sequence thatguarantees complete shells for each generation, leading to polymers that are mono-disperse. This property of dendrimers makes it particularlynatural to coarsen interactions in order to simulate dynamic processes occurring at larger length and longer time scales. In this paper, wedescribe methods to construct 3-dimensional molecular structures of dendrimers (Continuous Con®guration Boltzmann Biased direct MonteCarlo, CCBB MC) and methods towards coarse graining dendrimer interactions (NEIMO and hierarchical NEIMO methods) and representa-tion 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 assembliescrystallizing to A15 colloidal structure or Pm6m liquid crystals. q 2001 Elsevier Science Ltd. All rights reserved.Keywords: Dendrimers; Topology; Polymers1. IntroductionDendrimers and hyperbranched polymers represent anovel class of structurally controlled macromoleculesderived from a branches-upon-branches structural motif[1,2]. Dendrimers are well de®ned, highly branched macro-molecules that radiate from a central core and are synthe-sized through a stepwise, repetitive reaction sequence thatguarantees complete shells for each generation, leading topolymers that are monodisperse [3]. The synthetic proce-dures developed for dendrimer preparation permit nearlycomplete control over the critical molecular design para-meters such as size, shape, surface/interior chemistry, ¯ex-ibility, and topology [1±3]. Synthetic techniques provedeffective include the Starburst divergent strategy of Tomaliaand coworkers [1,2], the convergent growth strategy ofFrechet and coworkers [4±7], and the self-assembly strategyof Zimmerman and coworkers [8]. These methods haveproved effective in generating macromolecules with aunique combination of properties [9±14].The geometric characterization of dendrimer structurehas lagged and hence retarded the rapid progress in synth-esis and design. The problem is that dendrimers possess anenormous number of energetically permissible conforma-tions, and in solution there is frequent interchange betweenthem. The diffraction techniques yield little structure infor-mation. Also a number of generations involve the samemonomers, making it dif®cult to extract precise informationabout the local structure from infrared or NMR experiments.Thus the most precise experimental data about overall struc-ture comes from size exclusion chromatography (SEC). Themain experimental data about the geometric character ofparticular sites has come from NMR relaxation times formolecules that partially penetrate into the dendrimer [15].A particular advantage of using theory is that the proper-ties of new materials can be predicted in advance of experi-ments. This allows the system to be adjusted and re®ned soas to obtain the optimal properties before the arduousexperimental task of synthesis and characterization.However, there are signi®cant challenges in using theory123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112Computational and Theoretical Polymer Science 00 (2001) 000±000CTPS2221089-3156/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved.PII: S1089-3156(01)00026-5www.elsevier.nl/locate/ctps* Corresponding author.E-mail address: [email protected] (T. Cagin).Computational and Theoretical Polymer Science ± Model 5 ± Ref style 3 ±AUTOPAGINATION 2 24-04-2001 17:22 allapAldenUNCORRECTED PROOFto predict accurate properties of functional dendritic materi-als. Below we describe some recent developments in thearea of dendrimers and molecular modeling applicationsto a list of dendritic polymers: PAMAM, stimuli responsivepolymers, and colloidal crystals of self assembled dendri-mers. The paper is organized as follows: In Section 2, webrie¯y describe the Continuous Con®gurational BoltzmannBiased (CCBB) direct Monte Carlo method [16,17] used inbuilding the 3-dimensional molecular representations of thedendrimers used in this study, then the NEIMO and hier-archical NEIMO strategy [18±20]. In Section 2.3 wedescribe Poisson±Boltzmann (PB) and Surface GeneralizedBorn (SGB) approaches for accurate and ef®cient treatmentof continuum solvation in molecular dynamics simulation ofpolymers. Finally, in Section 3 we describe the molecularmechanics and molecular dynamics applications on variousdendrimers utilizing these methods.2. Methods2.1. The CCBB direct Monte Carlo method for dendrimersTo predict the properties of polymers, it is necessary todetermine an ensemble of conformations highly populatedat the temperature and pressure of interest. An ef®cientmethod for predicting these conformations is by usingMonte Carlo (MC) sampling. CCBB MC is an improvedmethod that was developed for this purpose [16±17]. Wehave taken advantage of this method to generate energeti-cally preferable 3-dimensional molecular structures ofvarious dendrimers.The CCBB direct Monte Carlo method is developed onthe basis of independent rotational sampling (IRS) method.In the IRS method, torsional degrees of the polymer chainsare sampled using a weighting function based on the Boltz-mann factor of the torsion energy. The normalized torsionweighting
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