Spatial segregation of mixed-sized counterions in dendritic polyelectrolytes

Langevin dynamics simulations are utilized to study the structure of a dendritic polyelectrolyte embedded in two component mixtures comprised of conventional (small) and bulky counterions. We vary two parameters that trigger conformational properties of the dendrimer: the reduced Bjerrum length, $$\lambda _B^*$$ λ B ∗ , which controls the strength of electrostatic interactions and the number fraction of the bulky counterions, $$f_b$$ f b , which impacts on their steric repulsion. We find that the interplay between the electrostatic and the counterion excluded volume interactions affects the swelling behavior of the molecule. As compared to its neutral counterpart, for weak electrostatic couplings the charged dendrimer exists in swollen conformations whose size remains unaffected by $$f_b$$ f b . For intermediate couplings, the absorption of counterions into the pervaded volume of the dendrimer starts to influence its conformation. Here, the swelling factor exhibits a maximum which can be shifted by increasing $$f_b$$ f b . For strong electrostatic couplings the dendrimer deswells correspondingly to $$f_b$$ f b . In this regime a spatial separation of the counterions into core–shell microstructures is observed. The core of the dendrimer cage is preferentially occupied by the conventional ions, whereas its periphery contains the bulky counterions.

Polyelectrolyte chain at thermal equilibrium: A comparison between the density functional theory framework (DFT) and the molecular dynamic simulations (MD)

ABSTRACTBy means of the density functional theory framework (DFT) as well as the molecular dynamic simulations (MD), a polyelectrolyte chain (PE) in the good solvent conditions at thermal equilibrium is studied. The strength of the electrostatic interactions is varied by the Bjerrum length of the solvent. It turns out that average extension of a PE scales with the degree of polymerization, very much similar to a neutral polymer chain in good solvent. Remarkably, the difference between a PE and a neutral chain appears to be solely in the correlations among monomers which are stored in the Virial coefficients. Interestingly, upon increasing the Bjerrum length of solvent, the chain shrinks. This outcome is confirmed by the DFT framework as well as the MD simulations.SIGNIFICANCEThe significance of this study is that it strongly criticizes the idea (already mentioned in T. Kreer, Soft Matter, 12, 3479 (2016)) that the PEs behave similar to a neutral ideal chain. This study could be useful in our understanding of biopolymers.

Polymer Conformations, Entanglements and Dynamics in Ionic Nanocomposites: A Molecular Dynamics Study

We investigate nanoparticle (NP) dispersion, polymer conformations, entanglements and dynamics in ionic nanocomposites. To this end, we study nanocomposite systems with various spherical NP loadings, three different molecular weights, two different Bjerrum lengths, and two types of charge-sequenced polymers by means of molecular dynamics simulations. NP dispersion can be achieved in either oligomeric or entangled polymeric matrices due to the presence of electrostatic interactions. We show that the overall conformations of ionic oligomer chains, as characterized by their radii of gyration, are affected by the presence and the amount of charged NPs, while the dimensions of charged entangled polymers remain unperturbed. Both the dynamical behavior of polymers and NPs, and the lifetime and amount of temporary crosslinks, are found to depend on the ratio between the Bjerrum length and characteristic distance between charged monomers. Polymer–polymer entanglements start to decrease beyond a certain NP loading. The dynamics of ionic NPs and polymers is very different compared with their non-ionic counterparts. Specifically, ionic NP dynamics is getting enhanced in entangled matrices and also accelerates with the increase of NP loading.

Density functional theory for charged fluids

Our improved DFT avoids the unphysical layer-by-layer phase predicted by a previous DFT for a moderately large Bjerrum length.

Underscreening in concentrated electrolytes

Screening of a surface charge by an electrolyte and the resulting interaction energy between charged objects is of fundamental importance in scenarios from bio-molecular interactions to energy storage. The conventional wisdom is that the interaction energy decays exponentially with object separation and the decay length is a decreasing function of ion concentration; the interaction is thus negligible in a concentrated electrolyte. Contrary to this conventional wisdom, we have shown by surface force measurements that the decay length is an increasing function of ion concentration and Bjerrum length for concentrated electrolytes. In this paper we report surface force measurements to test directly the scaling of the screening length with Bjerrum length. Furthermore, we identify a relationship between the concentration dependence of this screening length and empirical measurements of activity coefficient and differential capacitance. The dependence of the screening length on the ion concentration and the Bjerrum length can be explained by a simple scaling conjecture based on the physical intuition that solvent molecules, rather than ions, are charge carriers in a concentrated electrolyte.

Polymeric Electrolytes and Polyelectrolytes: Salt Concentration and Domain Effects on Conductivity

Solvent-free polymer electrolytes and polyelectrolytes are usually studied at quite high ionic concentrations, (into the range above 1M). Under these conditions, correlation effects arising from ion-polymer and ion-ion interactions are expected to be important in the mechanism of conductivity. We sketch some specific ionic effects, separating those actittg on the mobility from those effecting carrier concentration. Mobility effects include reduction of the fluidity due to the effective cross-linking by cations, screening of applied fields due to high ionic concentrations, frictional drag due to counterion motion, and in some polymer hosts, lowered local availability of cation solvation sites due to reduction of the number of coordinating basic oxygens. Reduction of the carrier density from its stoichipmetric value can be discussed in terms of a generalized ion-pairing model. Though the concentrations usually studied are so high that Debye-Huckel theory is invalid and the stoichiometric average cation-anion separation is smaller than the Bjerrum length (a situation in which ordinary electrolyte theory considers all ions paired), nevertheless consideration in terms of contact ion pairs, solvent separated ion pairs and mean stoichiometric separation can be used to compute the effective concentration of carriers. Estimates based on an electrostatic continuum, cavity model for the binding energy of a pair describe the reduction of effective carrier number observed in poly (propylene oxide) materials.