Theoretical Study Of Anomalous Intrinsic Viscosity For Dendrimers

Dendrimers form a new class of polymeric material with promising applications in a wide range of areas: specialty fluids, biomedical materials, nano-material, drug-delivery, genetic engineering, etc. The richness of their properties has been the subject of extensive theoretical, experimental and simulation studies. Some of the applications of dendrimers rely on their unique rheological behaviors. A key property characterizing the rheological behaviors of polymer solutions is the intrinsic viscosity. However, the intrinsic viscosity of dendrimers in solution shows several anomalous behaviors that have hitherto not been explained within existing theoretical frameworks of either Zimm or Rouse. To date, except that the Fox-Flory formula can capture the existence of a maximum in intrinsic viscosity, there are no theories that can capture all the anomalous behaviors, let alone producing agreement with experimental data with acceptable accuracy.In this paper we calculate the radial segmental density profile of dendrimers not only used the freely jointed chain model and Gaussian chain model without consideration of excluded volume effect but also used the self-consistent mean field method with consideration of excluded volume effect. And we propose a simple two-zone model for dendrimers based on the combination of Zimm and Rouse description of the intrinsic viscosity, which avoids the lack of self-similarity (scale invariance) between the different generations of dendrimers, Multi-body and"shielding"effects due to the presence of a dense core which effectively traps the solvent molecules in the inner core region and shields the hydrodynamic interactions between monomers in the outer region, and no holding the proportionality relationship between radius of gyration and radius of viscosity or between hydrodynamic radius and radius of viscosity for dendrimers.Furthermore, we establish a simple formula of intrinsic viscosity for dendrimers, which captures these three anomalous behaviors for [η], such as, (i) with increasing number of generations G, [η] passes through a maximum value; (ii) the generation number G for the tridendrons at which [η] reaches a maximum is less than that for the monodendrons; (iii) [η] of the tridendrons is higher than that of the monodendrons at small G, but lower at higher G, and yields reasonably good quantitative agreement with experimental data by Fréchet and co-workers.In addition, we physically elucidate why the structure of dendrimers exhibits the anomalous intrinsic viscosity and reveal the fact that the intrinsic viscosity should reflect the ability of the dendrimer to drag solvent along. Finally, we clarify the maximum of the intrinsic viscosity versus the generation corresponds to the maximum capacity of dendrimer to drag solvent molecules, an important property for applications as carrier materials and rheology modifiers.