Dendrimer viscosity

Unlike linear or ordinary branched polymers, dendrimers display intrinsically low viscosity, even at high mass. As standard polymeric molecules increase in mass and size, their viscosity normally increases continually. With dendrimers, viscosity increases only up to about the fourth generation, after which it actually begins to decline (Mourey, 1992 Frechet, 1994). In addition, with control over the type of pendent groups that adorn the surface, dendrimers can maintain high solubility regardless of size. 

The somewhat spherical shape of dendimers gives them some different properties in comparison to more linear macromolecules. On a macroscopic level, dendimers act as ball bearings rather than strings. In solution, viscosity increases as molecular weight increases for linear polymers. With dendrimers, viscosity also increases with molecular weight up to a point after which viscosity decreases as molecular weight continues to increase. 

Due to dieir compact, branched structure and to die resulting lack of chain entanglement, dendritic polymers exhibit much lower melt and solution viscosity dian their lineal" counterparts. Low a-values in die Mark-Houwink-Sakurada intrinsic viscosity-molar mass equation have been reported for hyperbranched polyesters.198 199 Dendrimers do not obey diis equation, a maximum being observed in die corresponding log-log viscosity-molar mass curves.200 The lack of chain entanglements, which are responsible for most of the polymer mechanical properties, also explains why hyperbranched polymers cannot be used as diermoplastics for structural applications. Aldiough some crystalline or liquid... 

However, dendrimeric and hyperbranched polyesters are more soluble than the linear ones (respectively 1.05, 0.70, and 0.02 g/mL in acetone). The solution behavior has been investigated, and in the case of aromatic hyperbranched polyesters,84 a very low a-value of the Mark-Houvink-Sakurada equation 0/ = KMa) and low intrinsic viscosity were observed. Frechet presented a description of the intrinsic viscosity as a function of the molar mass85 for different architectures The hyperbranched macromolecules show a nonlinear variation for low molecular weight and a bell-shaped curve is observed in the case of dendrimers (Fig. 5.18). 

Dendrimers have distinctive properties, such as the ability to entrap small molecules in their core region and very low intrinsic viscosities in solution. Such properties require molecules to have achieved a particular size, and not all molecules with branches radiating from a core are large enough to develop the characteristic properties of true dendrimers. Branched molecules below this critical size are called dendrons and are the equivalent in dendrimer chemistry of oligomers in polymer chemistry. 

The reason for the low intrinsic viscosities in solution is that dendrimers exist as tightly packed balls. This is by contrast with linear polymers, which tend to form flexible coils. The effect of this difference is that, whereas polymer solutions tend to be of high viscosity, dendrimer solutions are of very low viscosity. In fact, as dendrimers are prepared, their intrinsic viscosity increases as far as the addition of the fourth monomer unit to growing branches (the so-called fourth generation), but this is the maximum value that the viscosity reaches, and as the side chains grow beyond that, the viscosity decreases. 

Mourey, T.H., Turner, S.R., Rubenstein, M., Frechet, J.M.J., Hawker, C.J., and Wooley, K.L. (1992) Unique behavior of dendritic macromolecules Intrinsic viscosity of polyether dendrimers. Macromolecules 25, 2401-2406. 

Parallel studies on PAMAM dendrimers, the Frechet type polyether den-drons, and other dendrimer families have generated an extensive list of unique properties driven by the dendritic state/ Figure 1.18 compares several significant physical property differences between the linear and dendritic topologies related to conformations, crystallinity, solubilities, intrinsic viscosities, entanglement, diffusion/mobility and electronic conductivity. 

Frechet [49, 89] was the first to compare viscosity parameters for (A) linear topologies, as well as (B) random hyperbranched polymers and (C) dendrimers. More recently, we reported such parameters for (D) dendrigraft polymers [111] as shown in Figure 1.19. It is clear that all three dendritic topologies behave differently than the linear. There is, however, a continuum of behavior wherein random hyperbranched polymers behave most nearly like the linear systems. Dendrigrafts exhibit intermediary behavior, whereas dendrimers show a completely different relationship as a function of molecular weight. 

Figure 1.19 Comparison of intrinsic viscosities (log (f/)) versus molecular weight (log M) for (A) linear, (B) random hyperbranched, (C) dendrimers and (D) dendrigraft topologies. Data for A, B, C adapted from Frechet etal.. Ref. 49.

Figure 14.2 Dependence of intrinsic viscosity, [ /], on generation for PAMAM, PPI and PBzE dendrimers. Data for PBzE monodendrons are included for comparison...

Figure 14.6 Dependence of dendri mer sol ution viscosity, r, on shear rate, y, for the 40% wt solutions of the first seven generations, G, of PAMAM dendrimers in ethylenediamine solvent at 25°C.

Figure 14.7 Dependence of the zero-shear viscosity, uo, on molecular weight, M, for different dendrimer systems. (1) Dendrimers of different chemical composition but in the same state (i.e. PAMAM, PPI and PBzE dendrimers in bulk D, C and E, respectively). (2) Compositionally identical dendrimers (i.e. PAMAMs) in solutions and in the bulk state (A, B and D, respectively). (3) Compositionally identical dendrimers and linear polymers of comparable molecular weights (i.e. PAMAMs in the bulk state D and F, respectively)...

Figure 14.8 Generational dependence of relative viscosity, tv, on solution volume fraction for the first six generations, G, of PAMAM dendrimers in ethylenediamine (EDA) in comparison with theoretical predictions of Krieger (A), Eiler (B) and Mooney (C) hard sphere models (according to ref. [5])...

Consistent with the Newtonian flow of concentrated PAMAM solutions, it was found that all three types of dendrimers [40, 41, 50] under steady-shear conditions, and both PAMAMs [40] and PPIs [50] under creep [16,50] showed typical viscous behavior at all applied stress levels and testing temperatures. For example, as illustrated in Figure 14.9 [40], all of the first seven generations of PAMAMs showed constant viscosities over the entire ranges of shear rates investigated, and in addition to this, there was no hysteresis between the forward and the reverse stress sweeps in steady shearing, indicating the absence of thixotropy. 

Figure 14.10 Master curves of steady shear viscosity, r (at lower shear rates) and complex viscosity, r (at higher frequencies) for the first seven generations of PAMAM dendrimers at 40°C in the bulk state...

It was also noted by Farrington and co-workers that the chemical nature of the end-groups may have a substantial effect on the viscosity of bulk dendrimers, even under iso-free volume conditions [49]. This seems consistent with the establishment of interdendrimer interactions and supramolecular organization at rest in the bulk state. However, as in most other areas of dendrimer rheology, more data are desirable before definite conclusions can be drawn. 

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