# Branching Defects in Dendritic Molecules: Coupling Efficiency and Congestion Effects

journal contribution

posted on 24.09.2013, 00:00 by Martin Kröger, A. Dieter Schlüter, Avraham HalperinAn 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,*g*_{max}. 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*n*_{g}, the number of junctions, and the number of defects for both*g*≤*g*_{max}and*g*>*g*_{max}, as well as*g*_{max}and its dependence on*P*. The branching polydispersity is characterized by the average number of junction–junction bonds,*X*_{g}^{eff}. For*g*<*g*_{max}and efficient synthesis*X*_{g}^{eff}is weakly reduced with respect to*X*, its value in defect-free molecules, and*n*_{g}∼ (*X*^{eff}– 1)^{g}increases exponentially. In the congested regime, at*g*>*g*_{max}, branching is strongly reduced, and*X*_{g}^{eff}slowly approaches 2 as*X*_{g}^{eff}– 2 ∼ 1/*g*while*n*_{g}eventually exhibits power law growth:*n*_{g}∼*g*^{3}for dendrimers and*n*_{g}∼*g*^{2}for dendronized polymers. The branching defects can be interrogated by different forms of end-group analysis utilizing the theory framework proposed.