Monte Carlo simulations of a charged dendrimer with explicit counterions and salt ions

Abstract

Static properties of a dendrimer with generation g = 5 with positively charged terminal groups in an athermal solvent are studied by lattice Monte Carlo simulations using the cooperative motion algorithm as the tossing scheme. The calculations are performed both for a salt-free system with neutralizing counterions and for a small amount of added monovalent and divalent salt. The full Coulomb potential and the excluded volume interactions between ions and beads are taken explicitly into account with the reduced temperature tau, the number of salt cations (anions) n(s), and salt valence z(s) as the simulation parameters. The bahaviour of the systems is analyzed by the mean effective charge per end-bead <Q>, Coulomb mean energy <E>, mean-square radius of gyration <R(g)(2)>, pair correlation functions g(alphabeta), and charge density rho(ch). The simulations show that for n(s)> or = 0 and decreasing tau: (a) there is encapsulation in the dendrimer and condensation onto the terminal groups of anions accompanied by a monotonic decrease in <Q> and <E> and by subsequent swelling and shrinking of the molecule; (b) encapsulation, condensation and shrinking are the most significant and swelling weaker for |z(s)| = 2; (c) penetration of salt cations into the dendrimer is minor when compared to that of anions; (d) rho(ch) is reduced and becomes negative close to the center of mass of the dendrimer and on its periphery; (e) for the considered n(s) > 0, unlike divalent salt ions the monovalent ones cause slight effects when compared to the salt-free case.

Theory and simulations of charged polymers: From solution properties to polymeric nanomaterials

“…Similar to the case of the linear chains, counterion condensation occurs with increasing value of the Bjerrum length and is accompanied by subsequent swelling and collapse of the dendrimer molecules [102,103]. The existence of such nonmonotonic conformational transformations is due to fine interplay between growing repulsions between charged end-beads and counterion condensation tendency because of attractive interactions between counterions and the terminal groups.…”

Mean field theory of charged dendrimer molecules

“…Adding charged groups to dendrimers was proposed as a way to achieve open core conformations desired for drug delivery applications. Such considerations have motivated a number of theoretical [17][18][19][20][21][22][23][24][25][26][27][28][29] and experimental [30][31][32][33][34] studies of charged dendrimer molecules. For instance, Welch and Muthukumar 17 used Monte Carlo simulations to show that the size and conformations of dendrimers with charged branch and terminal points are strongly dependent on the salt concentration.…”

Complexes Comprised of Charged Dendrimers, Linear Polyelectrolytes, and Counterions: Insight through Coarse-Grained Molecular Dynamics Simulations

“…What is more, as coarse-grained models are computationally considerably less demanding than atomistic descriptions, they can provide major added value in studies of generic properties of dendrimers. This idea has been employed very recently in cases where the aim has been to systematically consider effects due to the size and charge density of dendrimers, 25,26 the strength of electrostatic interactions, 22,23 and the concentration of salt and valency of salt ions 27 and counterions. 28 While there has been significant progress in molecular modeling of solvated charged dendrimers, considerably less attention has been paid to simulations of complexes between dendrimers and linear polyelectrolytes.…”

“…For this reason, a commonly used strategy is to consider more generic features of dendritic polyelectrolytes through (coarse-grained) models of lower resolution. These models go beyond the Debye-Hückel approximation, allowing one to describe ions explicitly [22][23][24][25][26][27][28] even if the solvent is of implicit nature. Furthermore, recent work 23,24 has shown how one can also account for the discrete nature of solvent through explicit nonpolar 23 and polar 24 solvent molecules.…”