Simulation of polyelectrolyte solutions. The density of bound ions

Confined polyelectrolytes: The complexity of a simple system

The interaction between polyelectrolytes and counterions in confined situations and the mutual relationship between chain conformation and ion condensation is an important issue in several areas. In the biological field, it assumes particular relevance in the understanding of the packaging of nucleic acids, which is crucial in the design of gene delivery systems. In this work, a simple coarse-grained model is used to assess the cooperativity between conformational change and ion condensation in spherically confined backbones, with capsides permeable to the counterions. It is seen that the variation on the degree of condensation depends on counterion valence. For monovalent counterions, the degree of condensation passes through a minimum before increasing as the confining space diminishes. In contrast, for trivalent ions, the overall tendency is to decrease the degree of condensation as the confinement space also decreases. Most of the particles reside close to the spherical wall, even for systems in which the density is higher closer to the cavity center. This effect is more pronounced, when monovalent counterions are present. Additionally, there are clear variations in the charge along the concentric layers that cannot be totally ascribed to polyelectrolyte behavior, as shown by decoupling the chain into monomers. If both chain and counterions are confined, the formation of a counterion rich region immediately before the wall is observed. Spool and doughnut-like structures are formed for stiff chains, within a nontrivial evolution with increasing confinement.

Counterion condensation and effective charge of poly(styrenesulfonate)

The effective charge of poly(styrenesulfonate) has been investigated by diffusion and electrophoresis nuclear magnetic resonance (NMR). While the electrophoretic mobility is determined in the electrophoresis NMR experiment, the hydrodynamic friction is determined from diffusion NMR using Einstein's formula. On the timescale of the NMR experiment a steady state is reached, which results from the force balance between the electric field and the hydrodynamic friction from that the effective charge is calculated without any further model. For the monomer and short polymers the effective charge is equal to the nominal charge, the difference increases with an increasing degree of polymerisation. Increasing the ionic strength of the solution leads to enhanced counterion condensation. If the dielectric constant of the solution is lowered, condensation of counterions is enhanced as well. A lowered effective charge results in reduced repelling forces along the polymer chain and thus in a more compact conformation of the polymer as reflected in the hydrodynamic size. The effective charge of poly(styrenesulfonate) has been studied experimentally as a function of the degree of polymerisation, of the ionic strength and the dielectric constant of the solution.

Polyelectrolyte condensation in bulk, at surfaces, and under confinement

In this review we discuss recent results from computer simulations based on coarse-grained polyion models representing aqueous solutions of polyelectrolytes. The focus will be directed to the conformation of the polyions and, in particular, their condensation in bulk, induced by multivalent ions and oppositely charged polyelectrolytes, at responsive surfaces and under confinement.

Coil-globule coexistence and compaction of DNA chains

In this work we discuss different factors governing coil-globule coexistence in the compaction process of DNA. We initially analyse the role played by fluctuations in the degree of binding of an external compacting agent in the conformational behavior of the chain backbone. The analysis relies both on Monte Carlo simulation results and simple statistical approaches. Compacting agents of various binding characteristics are taken into consideration and the degree of charge neutralization upon the chain is related to conformational indicators. Selected model systems comprising stiff chains in the presence of multivalent ions are employed to assess intrinsic single-chain conformational fluctuation, in the presence of external agents but not resulting from differences in binding. It is shown that trends found for a variety of compacting agents, including the extension of the coil-globule coexistence regions, can be rationalised on the basis of this analysis.

Polyelectrolytes in solutions with multivalent salt. Effects of flexibility and contour length

It has been experimentally observed that trivalent ions are capable of promoting compaction of semi-flexible polyelectrolyte chains. In this work we perform Monte Carlo simulations on single chain model systems with varying chain size and stiffness and evaluate the action of multivalent salt on the chain conformation. It is observed that longer chains tend to achieve relatively more compact conformations than shorter ones, and the dimensions of the collapsed structures do not significantly vary with contour length. The influence of contour length and intrinsic stiffness in the process of ion condensation is studied by analysis of the ion-ion nearest-neighbor distribution. The general trend is an increase of the degree of ion condensation as the chain length increases, in accordance with experimental evidence. A decreased importance of end-effects and, especially, larger volume charge densities are responsible for such behavior. The influence of chain stiffness is nontrivial, and depends on salt concentration. The results emphasize the complex nature of ion-correlation phenomena in flexible or semi-flexible chains and call for the development of more sophisticated analytical theories.