Interaction between Charged Cylinders in Electrolyte Solution; Excluded Volume Effect

Interactions between Rigid Polyelectrolytes Mediated by Ordering and Orientation of Multivalent Nonspherical Ions in Salt Solutions

Multivalent ions in solutions with polyelectrolytes (PEs) induce electrostatic correlations that can drastically change ion distributions around the PEs and their mutual interactions. Using coarse-grained molecular dynamics simulations, we show how in addition to valency, ion shape and concentration can be harnessed as tools to control rigid like-charged PE-PE interactions. We demonstrate a correlation between the orientational ordering of aspherical ions and how they mediate the effective PE-PE attraction induced by multivalency. The interaction type, strength, and range can thus be externally controlled in ionic solutions. Our results can be used as generic guidelines to tune the self-assembly of like-charged polyelectrolytes by variation of the characteristics of the ions.

Research Progress of the Ion Activity Coefficient of Polyelectrolytes: A Review

Polyelectrolyte has wide applications in biomedicine, agriculture and soft robotics. However, it is among one of the least understood physical systems because of the complex interplay of electrostatics and polymer nature. In this review, a comprehensive description is presented on experimental and theoretical studies of the activity coefficient, one of the most important thermodynamic properties of polyelectrolyte. Experimental methods to measure the activity coefficient were introduced, including direct potentiometric measurement and indirect methods such as isopiestic measurement and solubility measurement. Next, progress on the various theoretical approaches was presented, ranging from analytical, empirical and simulation methods. Finally, challenges for future development are proposed on this field.

Numerical Studies on Electrostatic Interaction Forces and the Free Energy between Parallel Colloidal Rods of Finite Size in Skewed Configurations

Formulas for interaction forces F(s) and the free energy G(s) between two parallel charged prismatic rods of various scaled values of d, ψ_s, and L in skewed configurations are obtained, where s is the lengthwise positional difference between the front-end faces of the respective rods, and d is the minimal distance between the opposing faces of the rods, ψ_s is the electric surface potential, L is the length of the rods. To obtain the free-energy function G(s), (i) 3D spatial distributions of the electric potential ψ around two rods were determined by numerically solving the nonlinear Poisson-Boltzmann equation with a finite element method, (ii) with the ψ distributions so determined, the lengthwise interaction electrostatic Maxwell stress tangential to the midplane between the rods was calculated to obtain the (discrete) s dependence of the stress, and (iii) by introducing two different fitting functions, the discrete s dependence was transformed into a continuous force function, F(s), which was then lengthwise integrated to derive G(s). It was found that the curves of G(s) linearly decreased with increasing s between 1 and L + 1 due to a localization of the stress. Although natural, it is of interest that the values of G(0) calculated for rods of various values of d, ψ_s, and L were in good agreement with those of the interaction free energy obtained in our preceding work by the widthwise integration of repulsive electrostatic forces normal to the midplane between the parallel rods in nonskewed configurations.

Numerical Studies on Electrical Interaction Forces and Free Energy between Colloidal Plates of Finite Size

By solving the nonlinear Poisson-Boltzmann (PB) equation with a finite element method (FEM), three-dimensional (3D) spatial distributions of the electric potential (ψ, scaled) in electrolyte solutions having two charged parallel finite plates (including cubes and prismatic rods) are determined for various separations (d, scaled by the Debye length, κ^-1), surface potentials (ψ_s), and plate dimensions (length × width × thickness, each scaled by κ^-1). The total interaction force between two plates, F, is the sum of the electrostatic double-layer (EDL) repulsion (the osmotic pressure, F_osm) and the Maxwell electrostatic stress (F_es). The EDL repulsion is estimated using the distribution of ψ not only between the facing surfaces of two parallel plates but also around the other extremities of the plates. The Maxwell stress (F_es) is localized near the extremities to act as a repulsive force on the midplane between the two plates. The ratio F_es/F is 0.07-0.5, depending on d, ψ_s, and dimensions. It is found that, with increasing dimensions, the total F values per unit area calculated for finite plates, F̃, decreasingly approach the exact ones for parallel infinite plates, F̃^inf; for example, at d = 1 and ψ_s = 5, the ratio F̃/F̃^inf is 2.83 for plates with dimensions of 1 × 1 × 1 and 1.18 for plates of 10 × 10 × 1. The repulsions arising from the extremities cannot be neglected for plates with dimensions <10 × 10 × 1. Furthermore, the total interaction forces (F) are calculated at a series of discrete d values, respectively, for parallel plates. We introduce a force fitting function, F_f(d), with parameters that can be determined so that F_f(d) fits well to the calculated serial F values. By integrating the F_f(d), we obtain the interaction free energy, G(d), for finite parallel plates that consists of two Γ functions.

Multivalent counterions induced attraction between DNA polyelectrolytes

In this paper we study the electrostatic attraction between two parallel rodlike DNA polyelectrolytes induced by neutralizing multivalent counterions at the zero temperature limit. The counterions crystallize on the charged surfaces of DNA so that we can handle the system by using the Wigner crystal lattice model. We derived the 3D ground state configuration of counterions with minimized energy by use of the gradient descent method, and calculated the interaction between two DNA cylinders with divalent or trivalent counterions when they approach. The results show that the complex ground state configuration of counterions plays a key role in determining the caused attraction. The counterions form three-dimensional Wigner crystals on each cylinder at large separation. When the cylinders are brought together, some counterion lines will move towards the inner region and lead to strong attraction. The calculated interaction from our model is in good agreement with the simulation result, however, the single particle approximation considerably overestimates the attraction.

Counterions in the ground state partially condense in the intervening region of two approaching DNA cylinders and result in attraction.

Interaction between nanoparticles and charged phospholipid membranes

Charged lipids in cell membranes and subcellular organelles are arranged in the form of a bilayer with the hydrocarbon tails sequestered away from the water and the polar head groups exposed to the aqueous environment. Most of them bear net negative charges leading to the negatively charged cell membranes. Charged lipid-lipid and lipid-protein interactions are generally dynamic and heavily depend on their local molecular concentrations. To examine the electrostatic properties of charged lipid layers in contact with an electrolyte solution, we incorporate the single chain mean field theory with Poisson-Boltzmann theory to explore the equilibrium structure of charged phospholipid membranes. Using the three bead coarse-grained model we reproduced the essential equilibrium properties of the charged phospholipid bilayer. We also investigate the influence of the mobile ions on the thickness of the layer, the area per lipid (APL), and the electrostatic potential of the membrane. Then we investigate the attraction-repulsion property of two charged nanoparticles which are stuck on the charged lipid molecules surrounded with mobile ions. After that we simulated the interaction between the Pleckstrin homology domain (PH domain) of Akt and the cytoplasmic membrane. Taking into account the electrostatic interaction, we observe the structure changes of the membrane at different concentrations of mobile ions in its equilibrium state. Also we discuss the influence of mobile ions on the size of the pore opened in the membrane by the charged protein. Such an observation may shed light on the activation of oncogenic Akt (or protein kinase B) around the membrane at the molecular level.