Computer simulations of hyperbranched polymers: The influence of the Wiener index on the intrinsic viscosity and radius of gyration

Abstract

The influence of the Wiener index on solution properties of trifunctional hyperbranched polymers has been investigated using Brownian dynamics simulations with excluded volume and hydrodynamic interactions. A range of degrees of polymerization ͑N͒ and degrees of branching ͑DB͒ were used. For each DB and N, several molecules with different Wiener indices ͑W͒ were simulated, where W depends on the arrangement of branch points. The intrinsic viscosity and the radius of gyration (R g ) of HPs were both observed to scale with W at a constant N via a power law relationship, as found in the literature. Through their relationships to W, an expression relating intrinsic viscosity to R g was obtained. This relationship is found to fall centrally between the predictions of Flory and Fox for linear polymers and that of Zimm and Kilb for branched polymers. Molecular shape in solution is also found to depend on W and N, as observed through the W dependence of the ratio of R g to the hydrodynamic radius, R h .

Thermotropic Ionic Liquid Crystals via Self-Assembly of Cationic Hyperbranched Polypeptides and Anionic Surfactants

“…Results based on FTIR analysis were further confirmed by 1 H NMR spectroscopy, which allowed calculating the degree Because of poor solubility in common NMR solvents, the degree of loading for the C18 complex could not be determined. For the C8 and C12 complexes, the degrees of loading were close to 1, independent of the molecular weight of the polymer and the ratio of surfactant addition as shown in Table 1 40,41 In the present study, we have used small-angle X-ray scattering to determine the radius of gyration of both the HBPLs and HBPL-surfactant complexes in good solvent conditions. The HBPLs are soluble in both water and methanol.…”

Shear-induced effects in hyperbranched-linear polyelectrolyte complexes

“…20,26,33 Moreover, subtle differences in their rheological properties can be observed depending on the details of their branching topology. 29 In the same context, a direct link between the geometrical characteristics of these systems and the manifestation of changes in the intrinsic and shear viscosity has been established; it was found that the onset of the shear-thinning regime practically coincides with a prominent change in their geometrical features, suggesting that the analysis of shape parameters could be used as an indicator of expected changes in the rheological properties and vice versa. 26,33 The mechanisms involved in the manifestation of static and dynamic properties in noncovalent complexes between hyperbranched molecules and linear polyelectrolytes in equilibrium have been investigated in detail by means of computer simulations.…”

“…29,47 HPs with total number of beads corresponding to generations 2, 3, 4, or 5 of perfect dendrimers were utilized. DB of all the HP structures is chosen to be equal to 0.5 which stands between perfect dendrimer and linear chain.…”

“…[24][25][26][27][28][29] The transition from the Newtonian to the shear-thinning regime occurs at higher shear rates, while in the Newtonian regime they exhibit a lower viscosity compared to LP systems of comparable molecular weight. [30][31][32] These observations have been attributed to their highly branched structure which drastically affects their deformability and their final shape under shear flow.…”

Statistical properties of linear-hyperbranched graft copolymers prepared via “hypergrafting” of ABm monomers from linear B-functional core chains: A molecular dynamics simulation

“…The Wiener index and the path lengths can be used to compare densities of trees. Even though it can not be measured experimentally, it has been shown to correlate reasonably with properties such as density, viscosity and melting point [48][49][50]. For a linear chain consisting of N + 1 vertices, the Wiener index is given by W = 1 6 N (N + 1)(N + 2) and hence scales as W ∼ N 3 [51].…”