| An analytical model supplemented by Monte Carlo simulations specifies the statistics of branching defects in dendritic molecules as a function of the generation g as well as the maximal g for which defect free synthesis is possible, gmax. The defects arise because of (i) imperfect coupling efficiency characterized by an constant fraction P ≤ 1 of successful add-on reactions in the absence of excluded volume effects, and (ii) packing constraints associated with steric congestion at high g when the maximal density is approached. The model specifies ng, the number of junctions, and the number of defects for both g ≤ gmax and g > gmax, as well as gmax and its dependence on P. The branching polydispersity is characterized by the average number of junction-junction bonds, Xgeff. For g < gmax and efficient synthesis Xgeff is weakly reduced with respect to X, its value in defect-free molecules, and ng ~ (Xeff-1)g increases exponentially. In the congested regime, at g > gmax, branching is strongly reduced and Xgeff slowly approaches 2 as Xgeff-2 ~ 1/g while ng eventually exhibits power law growth: ng ~ g3 for dendrimers and ng ~ g2 for dendronized polymers. The branching defects can be interrogated by different forms of end group analysis utilizing the theory framework proposed.
for LaTeX users @article{MKroger2013-46,
author = {M. Kr\"oger and A. D. Schl\"uter and A. Halperin},
title = {Branching defects in dendritic molecules: Coupling efficiency and congestion effects},
journal = {Macromolecules},
volume = {46},
pages = {7550-7564},
year = {2013}
}
\bibitem{MKroger2013-46} M. Kr\"oger, A.D. Schl\"uter, A. Halperin,
Branching defects in dendritic molecules: Coupling efficiency and congestion effects,
Macromolecules {\bf 46} (2013) 7550-7564.MKroger2013-46
M. Kr\"oger, A.D. Schl\"uter, A. Halperin
Branching defects in dendritic molecules: Coupling efficiency and congestion effects
Macromolecules,46,2013,7550-7564 |
mk@mat.ethz.ch
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