"Ordered" structure in ionic dilute solutions: dendrimers with univalent and bivalent counterions

Solution properties of star polyelectrolytes having a moderate number of arms

We investigate polyelectrolyte stars having a moderate number of arms by molecular dynamics simulations of a coarse-grained model over a range of polyelectrolyte concentrations, where both the counter-ions and solvent are treated explicitly. This class of polymeric materials is found to exhibit rather distinct static and dynamic properties from linear and highly branched star polyelectrolyte solutions emphasized in past studies. Moderately branched polymers are particle-like in many of their properties, while at the same time they exhibit large fluctuations in size and shape as in the case of linear chain polymers. Correspondingly, these fluctuations suppress crystallization at high polymer concentrations, leading apparently to an amorphous rather than crystalline solid state at high polyelectrolyte concentrations. We quantify the onset of this transition by measuring the polymer size and shape fluctuations of our model star polyelectrolytes and the static and dynamic structure factor of these solutions over a wide range of polyelectrolyte concentration. Our findings for star polyelectrolytes are similar to those of polymer-grafted nanoparticles having a moderate grafting density, which is natural given the soft and highly deformable nature of both of these "particles."

Deswelling and Electrolyte Dissipation in Free Diffusion of Charged PAMAM Dendrimers

The diffusion coefficient of charged PAMAM dendrimers was measured by fluorescence correlation spectroscopy in aqueous solution at submicromolar concentrations. The solution pH was varied for conditions ranging from a fully charged to neutral charge dendrimer to infer about electrostatic swelling in the dilute regime. The diffusion coefficient of generation G4 increases by as much as 20% between high and low charge conditions due to the combined effects of polyelectrolyte deswelling and loss of electrolyte dissipation. By taking into account the electrolyte dissipation in the friction factor, we have found that the observed deswelling corresponds to a change of hydrodynamic radius between 7-13% for generation G4 and about 12% for generation G7. Simulations of molecular dynamics of dendrimer G4 show that counterion uptake by the dendrimer structure upon full protonation induces a 16% increase of its radius of gyration. The change in dendrimer size is slightly larger than that previously reported from neutron scattering techniques, thereby suggesting that electrostatic swelling is more pronounced at dilute dendrimer concentration and low ionic strength. It is confirmed that even higher generations, which have more congested molecular structures, can experience some degree of conformational change in response to a change of the dendrimer charge density.

Modeling dendrimers charge interaction in solution: relevance in biosystems

Dendrimers are highly branched macromolecules obtained by stepwise controlled, reaction sequences. The ability to be designed for specific applications makes dendrimers unprecedented components to control the structural organization of matter during the bottom-up synthesis of functional nanostructures. For their applications in the field of biotechnology the determination of dendrimer structural properties as well as the investigation of the specific interaction with guest components are needed. We show how the analysis of the scattering structure factor S(q), in the framework of current models for charged systems in solution, allows for obtaining important information of the interdendrimers electrostatic interaction potential. The finding of the presented results outlines the important role of the dendrimer charge and the solvent conditions in regulating, through the modulation of the electrostatic interaction potential, great part of the main structural properties. This charge interaction has been indicated by many studies as a crucial factor for a wide range of structural processes involving their biomedical application. Due to their easily controllable properties dendrimers can be considered at the crossroad between traditional colloids, associating polymers, and biological systems and represent then an interesting new technological approach and a suitable model system of molecular organization in biochemistry and related fields.

Structure factor and thermodynamics of rigid dendrimers in solution

The "polymer reference interaction site model" (PRISM) integral equation theory is used to determine the structure factor of rigid dendrimers in solution. The theory is quite successful in reproducing experimental structure factors for various dendrimer concentrations. In addition, the structure factor at vanishing scattering vector is calculated via the compressibility equation using scaled particle theory and fundamental measure theory. The results as predicted by both theories are systematically smaller than the experimental and PRISM data for platelike dendrimers.

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

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.

Macromolecular Assemblies Based on Coupled Inclusion Complex and Electrostatic Interactions

Macromolecular assemblies are elaborated by mixing beta-cyclodextrin-containing polymer (polybetaCD), dextran sulfate polyanion (NaDxS), and cationic amphiphiles which are adamantane derivatives (Ada1 or Ada2) in aqueous medium. These components are assembled via coupled inclusion complex interactions (adamantyl group with cyclodextrin cavity) and electrostatic attractive interactions (positive charges of Ada with negative charge of NaDxS). The structural properties are studied by viscometry and small angle neutron scattering. Ternary aggregates with larger size and lower compacities are observed as the cation concentration is increased, until phase separation occurs. The results are in good agreement with a core-shell association mechanism, the core being made of one polybetaCD chain, the shell of NaDxS chains, and the Ada amphiphiles being distributed more or less homogeneously inside the cyclodextrin cavities. The nature of the Ada counterions has a strong influence on the association as Ada1 with I(-) counterions give smaller and less compact aggregates than Ada2 with Br(-) counterions.

Influence of mixed and multivalent counterions in overcharging of DNA-like spherocylindrical macroions

The influence of multivalent and mixed valency counterions on the ground-state energetics of overscreening of a core DNA-like model (sphero)cylindrical macroion is investigated using an earlier developed energy minimization numerical simulation algorithm. The effects of mono-, di-, tri-, and tetravalent counterions, and mixed valency (mono- plus di-) counterions are compared and contrasted. It is seen that the depth of the minimum in the excess ground-state energy (over the neutral reference state) versus the number of overcharging counterions increases as counterion valency changes from mono- to tetra- testifying to the efficiency of the overcharging process due to multivalent counterions. The influence of (i) the presence of mixed valency counterions and (ii) counterion size on the energetics is also investigated.