Branching Defects in Dendritic Molecules: Coupling Efficiency and Congestion Effects
journal contributionposted on 24.09.2013, 00:00 by Martin Kröger, A. Dieter Schlüter, Avraham Halperin
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 a 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.