Understanding polyelectrolyte solutions: Macroion condensation with emphasis on the presence of neutral co-solutes

Application of the symmetric Poisson-Boltzmann theory to a model colloidal mixture

A symmetric Poisson-Boltzmann theory is used to analyse the structure of a primitive model colloidal system which contains either 4 or 6 components. The approach symmetrizes the pair distribution function gij(r) between two asymmetric charged species with respect to an interchange of the indices. Good agreement is found with molecular dynamics simulation structural properties when the exclusion volume term is modelled by the Percus-Yevick uncharged hard sphere radial distribution function.

Surface charging parameters of charged particles in symmetrical electrolyte solutions

Surface electric charge of dispersed particles is an essential determinant of physicochemical properties, coagulation and flocculation processes, and stability of colloidal solutions. Size-dependence of surface potential, charge density, and total surface charge of suspended charged particles has recently received attention in the literature. Despite the clear significance of understanding such dependence, very few studies have been devoted to this problem, with contradictory results of the relationship type. Currently, there is no analytical formula to represent explicit relationships between surface charging parameters and particle size. This research work is directed at development of accurate physics-based formulas for quantification of curvature-dependence of surface potential, surface charge density, and total surface charge for cylindrical and spherical charged particles immersed in a symmetrical electrolyte solution. First, a non-dimensional approach is adopted to simplify the problems, overcoming the difficulty of dealing with multiple influential variables. Then, to reduce the degrees of freedom of the problems under consideration, Gauss's law is combined with the condition of electro-neutrality in an electrical double layer (EDL). Next, the resulting complex integral equations are solved to construct characteristic curves and to express the dimensionless surface charging parameters explicitly as a function of the dimensionless particle radius. The new theoretical expressions are founded on approximate analytical and numerical solutions of the nonlinear Poisson-Boltzmann (PB) equation in cylindrical and spherical geometries. Afterwards, the solutions of the non-dimensionalized problems are dimensionalized to derive accurate explicit closed-form expressions, describing how surface charging parameters are related to the radius of a charged particle, properties of the solution, and thermodynamic conditions. These analytical formulas enable researchers to properly determine surface potential, surface charge density, total surface charge, and radius of dispersed particles by characterizing only one of them. Finally, the validity of the commonly-held hypothesis that surface charge density is independent of particle size is examined at the end of this study.

Net fluid flow and non-Newtonian effect in induced-charge electro-osmosis of polyelectrolyte solutions

This paper reports an interesting net fluid flow in the induced-charge electro-osmosis (ICEO) of poly(sodium 4-styrenesulfonate) (NaPSS) solutions measured through microparticle image velocimetry (μPIV). The net fluid flow is attributed to the significantly unequal cations and poly-anions of NaPSS. Owing to the phase delay effect of ions, different flow patterns appear with the alternating electric field. The inflow velocity and outflow velocity are found to be unequal and their relative magnitude shows a dependence on the electric field strength. The ICEO velocity is positively correlated with the NaPSS concentration. As NaPSS introduces the non-Newtonian effect, the well-known quadratic relationship between ICEO velocity and electric field strength in Newtonian fluids breaks. The ICEO velocity varies differently with the electric field strength as the NaPSS concentration changes. These new findings can contribute to the understanding of ICEO of complex fluids, e.g., biofluids.

Note: Density functional theory for uniformly charged hard-sphere ions

The density function theory has been proposed for studying the structural properties of electrolytes containing uniformly charged hard-spherical ions. The calculated result shows good agreement with the corresponding Monte Carlo simulation data of Bohinc et al. [J. Chem. Phys. 145, 234901 (2016)]. The results confirm that the attraction between like-charged planar surfaces is the results of the intra-ionic correlation and depends strongly on the charge distribution of hard-sphere ions.

Model for a mixture of macroions, counterions, and co-ions in a waterlike fluid

We propose an integral equation theory for a mixture of macroions, counterions, and co-ions in a waterlike fluid in which all the components are accounted for explicitly. The macroions can carry positive and negative surface charges simultaneously, mimicking in this way the situation occurring in protein solutions. To solve this complex model numerically, we utilize the associative mean spherical approximation, developed earlier for low-molecular-mass charge-symmetric electrolyte solutions. To illustrate the potential of this approach, we present numerical results for various experimental conditions. Among the measurable properties we choose to calculate the osmotic coefficient, a quantity that reflects the stability of the solution. We show that the osmotic coefficient depends not only on the magnitude of the net charge on the macroion but also on its sign, as well as on the nature of the low-molecular-mass electrolyte present. These specific ion effects are the consequence of differences in hydration between the ions in solution and charged groups on the macroion.

Structure of spherical electric double layers containing mixed electrolytes: a systematic study by Monte Carlo simulations and density functional theory

The structure of spherical electric double layers in the presence of mixed electrolytes is studied using Monte Carlo simulation and density functional theory within the restricted primitive model. The macroion is modeled as an impenetrable charged hard sphere carrying a uniform surface charge density, surrounded by the small ions represented as charged hard spheres, and the solvent is taken as a dielectric continuum. The density functional theory uses a partially perturbative scheme, where the hard-sphere contribution to the one-particle correlation function is evaluated using weighted density approximation and the ionic interactions are calculated using a second-order functional Taylor expansion with respect to a bulk electrolyte. The Monte Carlo simulations have been performed in canonical ensemble. The system is studied at varying ionic concentrations, at different concentration ratios of mono- and multivalent counterions of mixed electrolytes, at different diameters of hard spheres, at different macroion radius, and at varying polyion surface charge densities. The theoretical predictions in terms of the density profiles and the mean electrostatic potential profiles are found to be in good agreement with the simulation results. This model study shows clear manipulations of ionic size and charge correlations in dictating a number of interesting phenomena relating to width of the diffuse layer and charge inversion under different parametric conditions.

Comparing the Predictions of the Nonlinear Poisson-Boltzmann Equation and the Ion Size-Modified Poisson-Boltzmann Equation for a Low-Dielectric Charged Spherical Cavity in an Aqueous Salt Solution

The ion size-modified Poisson Boltzmann equation (SMPBE) is applied to the simple model problem of a low-dielectric spherical cavity containing a central charge, in an aqueous salt solution to investigate the finite ion size effect upon the electrostatic free energy and its sensitivity to changes in salt concentration. The SMPBE is shown to predict a very different electrostatic free energy than the nonlinear Poisson-Boltzmann equation (NLPBE) due to the additional entropic cost of placing ions in solution. Although the energy predictions of the SMPBE can be reproduced by fitting an appropriatelysized Stern layer, or ion-exclusion layer to the NLPBE calculations, the size of the Stern layer is difficult to estimate a priori. The SMPBE also produces a saturation layer when the central charge becomes sufficiently large. Ion-competition effects on various integrated quantities such the total number of ions predicted by the SMPBE are qualitatively similar to those given by the NLPBE and those found in available experimental results.

The intranuclear environment

Many of the chapters in this volume are concerned with processes or structures inside the nucleus, and it is relevant to consider the properties of their environment, or rather of the multiple different and specific environments that must exist in local regions of the highly heterogeneous intranuclear space. Relatively little is known about the fundamental physical properties of these environments, and theoretical treatments of phenomena in such concentrated mixtures of charged macromolecules are complex and as yet poorly developed. Some of the phenomena that occur at the molecular level are unexpected and counterintuitive for biologists, although well known to colloid and polymer scientists; for example, the existence of short-range attractive forces between macromolecules or structures with like charges. As a background for the chapters that follow, we consider here some of the particular features of intranuclear environments, how they may influence processes and structures in the nucleus, and their implications for working with nuclei.

Interrelationship of steric stabilization and self-crowding of a glycosylated protein

In the eukaryotic cell, protein glycosylation takes place in the crowded environment of the endoplasmatic reticulum. With the purpose of elucidating the impact of high concentration on the interactions of glycoproteins, we have conducted a series of small-angle x-ray scattering experiments on the heavily glycosylated enzyme Peniophora lycii phytase (Phy) and its deglycosylated counterpart (dgPhy). The small-angle x-ray scattering data were analyzed using an individual numerical form factor for each of the two glycoforms combined with two structure factors, a hard sphere and a screened coulomb potential structure factor, respectively, as determined by ab initio analysis. Based on this data analysis, three main conclusions could be drawn. First, at comparable protein concentrations (mg/ml), the relative excluded volume of Phy was approximately 75% higher than that of dgPhy, showing that the glycans significantly increase excluded-volume interactions. Second, the relative excluded volume of dgPhy increased with concentration, as expected; however, the opposite effect was observed for Phy, where the relative excluded volume decreased in response to increasing protein concentration. Third, a clear difference in the effect of salinity on the excluded-volume interactions was observed between the two glycol forms. Although the relative excluded volume of dgPhy decreased with increasing ionic strength, the relative excluded volume of Phy was basically insensitive to increased salinity. We suggest that protrusion forces from the glycans contribute to steric stabilization of the protein, and that glycosylation helps to sustain repulsive electrostatic interactions under crowded conditions. In combination, this aids in stabilizing high concentrations of glycosylated proteins.

Nanoparticle-assembled capsule synthesis: formation of colloidal polyamine-salt intermediates

There is current interest in developing new synthesis strategies for multifunctional hollow spheres with tunable structural properties that would be useful in encapsulation and controlled release applications. A new route was reported recently, in which the sequential reaction of polyamines, multivalent anions, and charged nanoparticles leads to the formation of polymer-filled and water-filled organic/inorganic micron-sized structures known as nanoparticle-assembled capsules. This technique is unique among other capsule preparation routes, as it allows the rapid and scalable formation of robust shells at room temperature, in near-neutral water, and with readily available precursors. This nanoparticle assembly synthesis route involves two steps: the formation of polymer aggregates and the subsequent deposition of particles around the aggregates. The purpose of this paper is to understand in greater detail the noncovalent chemistry of the polymer-salt aggregation step. With poly(allylamine hydrochloride) (PAH) as the model polymer, aggregate formation was investigated as a function of charge ratio, pH, and time through dynamic light scattering, electrophoretic mobility measurements, chloride ion measurements, and optical microscopy. PAH formed aggregates by the cross-linking action of divalent and higher-valent anions above a critical charge ratio and in a pH range defined by the pKa values of PAH and the anion. The aggregates grew in size through coalescence and with growth rates that depended on their surface charge. Controlling polymer aggregate growth provided a direct and simple means to adjust the size of the resultant capsule materials.

Density functional theory for polyelectrolytes near oppositely charged surfaces

We report a nonlocal density functional theory of polyelectrolyte solutions that faithfully accounts for both short- and long-range correlations neglected in a typical mean-field method. It is shown that for systems with strong electrostatic interactions, the long-range correlations are subdued by direct Coulomb attractions, thereby manifesting strong local excluded-volume effects. The theory has also been used to describe the influence of the polyion chain length and small ion valence on charge inversion due to the adsorption of polyelectrolytes at an oppositely charged surface.

Effect of discrete macroion charge distributions in solutions of like-charged macroions

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on structural properties of aqueous solutions of like-charged macroions has been investigated by Monte Carlo simulations. Two discrete charge distributions have been considered: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both discrete charge distributions have been examined with fixed and mobile macroion charges. Different boundary conditions have been applied to examine various properties. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion and the effect increases with counterion valence. As a consequence, with mono- and divalent counterions the potential of mean force between two macroions becomes less repulsive and with trivalent counterions more attractive. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the potential of mean force between two macroions becomes more repulsive/less attractive.

Monte Carlo simulations of oppositely charged macroions in solution

The structure and phase behavior of oppositely charged macroions in solution have been studied with Monte Carlo simulations using the primitive model where the macroions and small ions are described as charged hard spheres. Size and charge symmetric, size asymmetric, and charge asymmetric macroions at different electrostatic coupling strengths are considered, and the properties of the solutions have been examined using cluster size distribution functions, structure factors, and radial distribution functions. At increasing electrostatic coupling, the macroions form clusters and eventually the system displays a phase instability, in analogy to that of simple electrolyte solutions. The relation to the similar cluster formation and phase instability occurring in solutions containing oppositely charged polymers is also discussed.

Theoretical study of catalytic effects in micellar solutions

The catalytic effect of charged micelles as manifested through the increased collision frequency between the counterions of an electrolyte in the presence of such micelles is explored by the Monte Carlo simulation technique and various theoretical approaches. The micelles and ions are pictured as charged hard spheres embedded in a dielectric continuum with the properties of water at 298 K with the charge on micelles varying from zero to z(m) = 50 negative elementary charges. Analytical theories such as (i) the symmetric Poisson-Boltzmann theory, (ii) the modified Poisson-Boltzmann theory, and (iii) the hypernetted-chain integral equation are applied and tested against the Monte Carlo data for micellar ions (m) with up to 50 negative charges in aqueous solution with monovalent counterions (c; z(c) = +1) and co-ions (co; z(co) = -1). The results for the counterion-counterion pair correlation function at contact, g(cc)(sigma(cc)), are calculated in a micellar concentration range from c(m) = 5 x 10(-)(6) to 0.1 mol/dm(3) with an added +1:-1 electrolyte concentration of 0.005 mol/dm(3) (for most cases), and for various model parameters. Our computations indicate that even a small concentration of a highly charged polyelectrolyte added to a +1:-1 electrolyte solution strongly increases the probability of finding two counterions in contact. This result is in agreement with experimental data. For low charge on the micelles (z(m) below -8), all the theories are in qualitative agreement with the new computer simulations. For highly charged micelles, the theories either fail to converge (the hypernetted-chain theory) or, alternatively, yield poor agreement with computer data (the symmetric Poisson-Boltzmann and modified Poisson-Boltzmann theories). The nonlinear Poisson-Boltzmann cell model results yield reasonably good agreement with computer simulations for this system.

Density-functional theory for the structures and thermodynamic properties of highly asymmetric electrolyte and neutral component mixtures

Density-functional theory (DFT) is applied to investigate the structural and thermodynamic properties of concentrated electrolyte and neutral component mixtures that are highly asymmetric in terms of both size and charge mimicking a crowded cellular environment. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The direct correlation functions are obtained from the analytical solutions of the mean-spherical approximation. In the context of a primitive model where biomacromolecules are represented by neutral or charged hard spheres and the solvent is represented by a continuous dielectric medium, this DFT is able to take into account both the excluded-volume effects and the long-ranged electrostatic interactions quantitatively. The performance of the theoretical method has been tested with Monte Carlo simulation results from this work and from the literature for the pair correlation functions, excess internal energies, and osmotic coefficients for a wide variety of aqueous dispersions of charged and neutral particles.