Computer Simulation of the Dynamics of Neutral and Charged Dendrimers

Abstract

Dynamic properties of dilute solutions of neutral and charged dendrimers with explicit excluded-volume, electrostatic, and hydrodynamic interactions have been investigated by Brownian dynamics simulation. Three different types of motions in dendrimers up to g = 5 generations have been considered: the motion of a dendrimer as a whole; the size and shape fluctuations (pulsations); the local reorientations of the individual monomers. The influence of the excluded-volume, electrostatic, and hydrodynamic interactions on these motions has been studied. The characteristic relaxation times have been compared with the theoretical predictions of the Rouse and Zimm models. The self-diffusion of a dendrimer can be described with the help of the preaveraged Zimm approach, and a dendrimer may be considered as an impenetrable sphere with the hydrodynamic radius R h. For both neutral and charged dendrimers the hydrodynamic radius is smaller than the gyration radius R g. The dynamics of the size fluctuations for a dendrimer with rigid spacers differs significantly from the theoretical predictions for a dendrimer with flexible spacers. The relaxation of these fluctuations is weakly sensitive to the presence of the hydrodynamic interactions, and the behavior of a dendrimer is close to that of an elastic body in a viscous medium. The local orientational mobility of individual monomers is significantly influenced by the ionization of the terminal groups.

Dynamics of Complexation of a Charged Dendrimer by Linear Polyelectrolyte: Computer Modelling

“…2. As for a single neutral dendrimer [14] the time dependence of for charged dendrimers in complexes with different linear PEs is close to linear, i.e. these ACFs decay exponentially.…”

“…3a together with the corresponding times for a linear chain in a complex and for a complex as a whole. Our previous simulations of both neutral and charged single dendrimers have shown [14] that the value of the corresponding relaxation time 2 g R τ is insensible to the dendrimer size. To explain this effect the dendrimer was represented as a viscoelastic spherical body [14].…”

“…As in the previous studies [12][13][14][15][16] we consider a bead-rod freely-joint model of a dendrimer and an oppositely charged linear PE chain, Fig. 1.…”

“…The main effect of the electrostatic interactions should be expected when the Debye length exceeds the dendrimer size. In the present study the sufficiently large value of = k -1 D r = 8.96l has been chosen (which corresponds to 2.2 mM aqueous salt concentration at 25 C), as was used by the authors previously for simulations of single charged dendrimers [13][14]. For the complexes where the dendrimer charge is compensated by the charge of the linear chain the counterions condensation should be small and is not taken into account in the present study.…”

“…All beads of a complex are characterized by the friction coefficient ζ . The finite-difference numerical scheme implemented here is based on the Ermak-McCammon equation [12][13][14][15][16]19].…”