Statistical properties of linear-hyperbranched graft copolymers prepared via "hypergrafting" of AB_m monomers from linear B-functional core chains: A Molecular Dynamics simulation

The reaction of $AB_m$ monomers (m=2,3) with a multifunctional B_f-type polymer chain ("hypergrafting") is studied by coarse-grained molecular dynamics simulations. The $AB_m$ monomers are hypergrafted using the slow monomer addition strategy. Fully dendronized, i.e., perfectly branched polymers are also simulated for comparison. The degree of branching DB of the molecules obtained with the "hypergrafting" process critically depends on the rate with which monomers attach to inner monomers compared to terminal monomers. This ratio is more favorable if the $AB_m$ monomers have lower reactivity, since the free monomers then have time to diffuse inside the chain. Configurational chain properties are also determined, showing that the stretching of the polymer backbone as a consequence of the "hypergrafting" procedure is much less pronounced than for perfectly dendronized chains. Furthermore, we analyze the scaling of various quantities with molecular weight M for large M (M>100). The Wiener index scales as $M^2.3$, which is intermediate between linear chains ($M^3$) and perfectly branched polymers ($M^2 \ln(M)$). The polymer size, characterized by the radius of gyration $R_g$ or the hydrodynamic radius $R_h$, is found to scale as $R_{g,h}~M^{\nu}$ with $\nu~0.38$, which lies between the exponent of diffusion limited aggregation ($\nu=0.4$) and the mean-field exponent predicted by Konkolewicz and coworkers ($\nu=0.33$).