Simulations of Terminally Charged Dendrimers with Flexible Spacer Chains and Explicit Counterions

Abstract

We study the properties of terminally charged dendrimers under systematic variation of the length of flexible spacers, accompanied by explicit counterions in an athermal solvent using Monte Carlo simulations based on the bond fluctuation model. In our study, both the full Coulomb potential and the excluded volume interactions are taken into account explicitly with the reduced temperature, τ, as the main control parameter. Our calculations confirm that counterions get localized in the molecules’ interior and, in particular, condense on the terminal groups as τ is lowered. This, in turn, affects the conformational properties of the molecules that swell at intermediate τ due to dominating repulsion between the terminal groups and shrink in the limit of high and low τ, respectively. Like for neutral dendrimers, we find a substantial decrease in monomer densities with the radial distance from the dendrimers’ center of mass and backfolding of the terminal groups toward the molecules’ interior. By means of the radius of gyration tensor, we conclude that the mean instantaneous shape of dendrimers is spherical for all τ inspected.

Counterion Condensation and Effective Charge of PAMAM Dendrimers

“…A number of simulations exists [11][12][13][14][15], studying the variation of pH or electrostatic interactions in particular on structure and dynamics of dendrimers. The influence of counterion condensation for generic dendrimer with a three functional core (as opposed to PAMAM dendrimers, which have a tetrafunctional core) and terminal charged cationic dendrimers has been studied in [13,14].…”

“…The influence of counterion condensation for generic dendrimer with a three functional core (as opposed to PAMAM dendrimers, which have a tetrafunctional core) and terminal charged cationic dendrimers has been studied in [13,14]. Both observed, that increasing strength of electrostatic interaction provokes counterion condensation, but no effective number of charges has been derived for the typically conditions of dendrimers in aqueous solutions.…”

Monte Carlo simulations of charged dendrimer-linear polyelectrolyte complexes and explicit counterions

“…[26][27][28] The systems we examine consist of two polyelctrolytes accompanied by their counterions: A G4 terminally charged dendrimer with the core of two bonded monomers, spacer length S = 1, and branching functionality f = 3, and an oppositely charged linear chain of varying length 10 ≤ N ch ≤ 80. More specifically, N t = 32 outermost dendrimer beads (terminal groups) out of 62 monomers in total, carry positive charges z = 1.…”

“…For details about the implementation of the BFM model for charged dendrimers, see our previous works. [26][27][28] The interactions we consider include the excluded volume between the monomers and the Coulomb energy between the charges. The former is accounted for by the BFM algorithm itself, whereas the latter is calculated using the Ewald summation method.…”

“…Compared with previous work we note that τ 0 cond for the isolated dendrimer (N ch = 0) is at about 0.75. 27,28 In Fig. 4(b) the same data are shown as functions of the chain length.…”