The Structure of Dendrimers with Charged Terminal Groups: Monte Carlo Simulations

Abstract

Taking into account the full Coulomb potential and the excluded volume interactions, properties of dendrimers with generations g = 5, 6 with charged terminal groups and counterions in an athermal solvent are examined by lattice Monte Carlo simulations. The study treats counterions explicitly and focuses on the local structure of the systems inspected by pair correlation functions g ab that provide information on distributions of monomers, terminal groups and ions in space at various temperatures T * . Special emphasis is placed on counterions and their role they play in causing conformational changes of the molecules. The simulations show that counterions penetrate the interior of the dendrimers, and there is a major increase in their concentration there as T * decreases. Some of them condense onto the terminal groups and a reduction in the mean effective charge Q of the dendrimers appears. Within the range of temperatures where the condensation (as a function of T * ) is sharp the molecules weakly swell up when compared to their size at the other temperatures. This kind of behaviour is also reflected by the distributions of monomers and terminal groups.

Simulations of Dendrimers with Flexible Spacer Chains and Explicit Counterions under Low and Neutral pH Conditions

“…In the following we assume that an ion is condensed when its distance from at least one charged unit is less than √6, a distance comparable with the average bond length in the BFM. This approach is widely used in studies on polyelectrolyte systems and has proved reasonable both for lattice and off-lattice simulations. − , A comparison of various methods has been given by Grass and Holm . We note that the peak-position of the correlation functions in Figure is nearly constant.…”

“…This approach is widely used in studies on polyelectrolyte systems and has proved reasonable both for lattice and off-lattice simulations. [20][21][22][23]59 A comparison of various methods has been given by Grass and Holm. 59 We note that the peak-position of the correlation functions in Figure 2 is nearly constant.…”

“…17,18 Actually, as the strength of electrostatic interactions increases both under neutral and low pH conditions counterions penetrate not only the molecule periphery but, in the first place, its interior. 15,[19][20][21][22][23][24][25][26] This leads to the reduction of the dendrimer effective charge, screening of electrostatic repulsion between charged monomers and nonmonotonous behavior of dendrimer size. Last but not least ions also play a crucial role in the formation of complexes comprised of charged dendrimers and linear polyanions and in self-organization in solutions of charged dendrimers, [27][28][29][30][31][32][33] though many important aspects of complexation such as dendrimer overcharging by linear polyelectrolytes have been revealed within the Debye-H€ uckel approach as well.…”

“…It is therefore apparent from previous studies that the degrees of freedom of counterions have to be taken into account explicitly for dendritic polyelectrolytes due to the importance of ion valence and trapping in the dendrimer volume, ion condensation and their effect on conformational changes of dendrimers. , Actually, as the strength of electrostatic interactions increases both under neutral and low pH conditions counterions penetrate not only the molecule periphery but, in the first place, its interior. ,− This leads to the reduction of the dendrimer effective charge, screening of electrostatic repulsion between charged monomers and nonmonotonous behavior of dendrimer size. Last but not least ions also play a crucial role in the formation of complexes comprised of charged dendrimers and linear polyanions and in self-organization in solutions of charged dendrimers, − though many important aspects of complexation such as dendrimer overcharging by linear polyelectrolytes have been revealed within the Debye−Hückel approach as well. − Obviously, it is dendrimer−DNA binding − in the first place, which being of immense interest in biosciences inspires theoretical investigations.…”

Theoretical and computational studies of dendrimers as delivery vectors

“…It indeed can reduce the computational load and easily handle the ion strength effect via tuning the value of k. However, it should be stressed that the Debye screening approximation has an important limitation when dealing with charged polymers in salt solution because it cannot capture the important nonlinear features, such as counterion condensation. [86][87][88][89][90][91][92] It is valid in situations where the separation between charges exceeds the Bjerrum length, but the condition breaks down easily in the case of dendrimer structures and multivalent salt ions. To overcome this limitation, Gurtovenko et al 93 employed MD simulations of charged dendrimers under neutral pH conditions with explicit counterions and solvent molecules under the penalty of computational cost.…”