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Revealing the ion distributions on a charged lipid membrane in aqueous solution under the influence of long-range interactions is essential for understanding the origin of the stability of the bilayer structure and the interaction between biomembranes and various electrolytes. However, the ion distributions and their dynamics associated with the phase separation process of the lipid bilayer membrane are still unclear. We perform coarse-grained molecular dynamics simulations to reveal the Na + and Cl - distributions on charged phospholipid bilayer membranes during phase separation. During the phase separation, cations closely follow the position of negatively charged lipids on a microsecond timescale and are rapidly redistributed parallel to the lipid bilayer. In the homogenous mixture of zwitterionic and negatively charged lipids, cations weakly follow negatively charged lipids, indicating the strong interaction between cations and negatively charged lipids. We also compare cation concentrations as a function of surface charge density obtained by our simulation with those obtained by a modified Poisson-Boltzmann theory. Including the ion finite size makes the statistical results consistent, suggesting the importance of the ion-ion interactions in aqueous solution. Our simulation results advance our understanding of ion distribution during phase separation.

In this study we derived a model for a multicomponent lipid monolayer in contact with an aqueous solution by means of a generalized classical density functional theory and Monte Carlo simulations. Some of the important biological lipid systems were studied as monolayers composed of head groups with different shapes and charge distributions. Starting from the free energy of the system, which includes the electrostatic interactions, additional internal degrees of freedom are included as positional and orientational entropic contributions to the free energy functional. The calculus of variation was used to derive Euler-Lagrange equations, which were solved numerically by the finite element method. The theory and Monte Carlo simulations predict that there are mainly two distinct regions of the electric double layer: (1) the interfacial region, with thickness less than or equal to the length of the fully stretched conformation of the lipid head group, and (2) the outside region, which follows the usual screening of the interface. In the interfacial region, the electric double layer is strongly perturbed, and electrostatic profiles and ion distributions have functionality distinct to classical mean-field theories. Based purely on Coulomb interactions, the theory suggests that the dominant effect on the lipid head group conformation is from the charge density of the interface and the structured lipid mole fraction in the monolayer, rather than the salt concentration in the system.

Mixtures of an anionic polyelectrolyte, poly(sodium methacrylate), NaPMA, and a neutral polymer, polyethylene glycol, PEG, were investigated by dynamic and static light scattering techniques at different concentrations and chain-lengths of PEG. The NaPMA standard with a narrow molecular weight distribution was chosen for the study. The so called slow-mode behaviour, characteristic of salt-free NaPMA solutions, vanishes as the simple salt, NaCl in this case, is added in a sufficient amount. However, in NaPMA-NaCl-PEG mixtures, the slow-mode signal is observed again. We assume that the dielectric constant of the mixture with PEG, which is substantially lower than that of pure water, causes the reappearance of the slow-mode signal through reinforced electrostatic interactions between NaPMA polyions. Monte Carlo simulations of a coarse-grained model of the system confirm stronger correlations between NaPMA molecules and thus qualitatively agree with experimental results.

The interaction between like-charged objects in electrolyte solutions can be heavily altered by the presence of multivalent ions which possess a spatially distributed charge. In this work, we examine the influence of stiff, multivalent zwitterionic polymers on the interaction between charged surfaces using a splitting field theory previously shown to be accurate for the weak to the intermediate to the strong electrostatic coupling regimes. The theory is compared to Monte Carlo simulations and good agreement is found between both approaches. For surface separations shorter than the polymer length, the polymers are mainly oriented parallel to the surfaces, and the surface-surface interaction is repulsive. When the surface separation is comparable to the length of polymers, the polymers have two main orientations. The first corresponds to the polymers adsorbed onto the surface with their centers located near to or in contact with the surface; the second corresponds to polymers which are perpendicular to the charged surfaces, bridging both surfaces and leading to an attractive force between them. Increasing the surface charge density leads to more pronounced attraction via bridging. At surface separations greater than the polymer length, the polymers in the center of the system are still mainly perpendicular to the surfaces, due to "chaining" between zwitterions that enable them to bridge the surfaces at larger separations. This leads to an attractive interaction between the surfaces with a range significantly longer than the length of the polymers.

A coarse-grained model of simple monovalent electrolyte solution in contact with a zwitterionic lipid layer in continuum solvent is studied by canonical Monte Carlo computer simulations and extended Poisson-Boltzmann theory. A structure of zwitterionic layer as well as concentration profiles of positively and negatively charged monovalent ions were obtained from simulations and compared to theoretical predictions. A relatively good agreement between the Monte Carlo computer simulations and theory was observed.

The silica particle interactions in the presence of spermidine were systematically investigated both from experimental and theoretical points of view. The hydrodynamic radii and the corresponding polydispersity indices of the colloidal silica particles were determined by dynamic light scattering (DLS) as a function of spermidine concentration. Whereas the effective size of the silica particles increases with increasing spermidine concentration (pointing to the particle aggregation), the polydispersity index first increases reaches a maximum and then further decreases with the increasing spermidine concentration. From the mobility measurements it was concluded that the increase in spermidine concentration causes less negative values of zeta potential, meaning that the adsorption of spermidine leads to the less negative silica surface. Moreover, Monte Carlo (MC) simulations also confirmed that the addition of spermidine reduces the repulsion between silica particles. The MC concentration profiles of spermidine close to the charged silica particle are in a very good agreement with the results obtained by theory. An important motivation for our study is the effectiveness of multivalent ions to coagulate colloidal suspensions; e.g., the multivalent ions are exploited in the water purification process.

Many separation processes are related to the behavior of ions close to charged surfaces. In this work, we examine uranyl ions, which can be considered as rod-like molecular ions with a spatially distributed charge, embedded in a system of like charged surfaces. The analysis of the system is based on an approximate field theory which is accurate from the weak to the strong electrostatic coupling regimes. The numerical results show that close to the charged surface the ions are oriented parallel to the surface, whereas at distances greater than half of the ion length, they are randomly oriented. Due to the restriction of the orientational degrees of freedom, the density of ions at the charged surface decreases to zero. For large surface charge densities, the force between like charged surfaces becomes attractive, as a result of charge correlations. The theoretical results are in good agreement with Monte Carlo simulation results.

A force between two equally charged surfaces depends on the composition of intervening solution. While the force is always repulsive for monovalent counterions, multivalent counterions turn the interaction into the attractive one. An example of the attraction between like charged surfaces is the aggregation of colloidal particles mediated by multivalent counterions with spatially separated charges. A model system represents the colloids by equally charged planar surfaces. In our consideration the intervening salt-free solution is composed of rod-like dimmers. Some of dimmers can be disconnected to monovalent ions. This model system was solved using the Monte Carlo (MC) simulations and the Poisson-Boltzmann (PB) theory, which was extended to deal with rigid complex ions. The study was made by varying a range of parameters including the surface charge density and the ratio of the number of monovalent counterions to the number of all counterions. The calculated pressure shows that with increasing surface charge density the lower fraction of dimeric counterions is needed to induce attractive force between surfaces. A good agreement between the MC simulations and the theoretical results was obtained.