Effect Of Counterion Condensation Research Articles

Transient electrophoresis of colloidal particles in a salt-free medium

A general theory is developed for the time dependent transient electrophoretic mobility of spherical colloidal particles in a salt-free liquid medium containing only counterions when a step external electric field is suddenly applied to the colloidal suspension. It is found that as in the case of the steady electrophoretic mobility in a salt-free medium, there is a certain critical value of the particle surface charge separating two cases, that is, the low-surface-charge case and the high-surface-charge case. In the latter case the counterion condensation takes place near the particle surface. For the low-surface charge case, the transient electrophoretic mobility agrees with that of a sphere in an electrolyte solution in the limit of very low electrolyte concentrations. For the high-surface-charge case, however, the transient mobility becomes independent of the particle surface charge because of the counterion condensation effects. A simple expression is derived for the ratio of the transient electrophoretic mobility to the steady electrophoretic mobility, which is found to take the same form irrespective of the magnitude of the particle surface charge. Using this equation, it is now possible to predict how the system will approach its final steady state.

Biodegradable Microembolics with Nanografted Polyanions Enable High-Efficiency Drug Loading and Sustained Deep-Tumor Drug Penetration for Locoregional Chemoembolization Treatment.

Transarterial chemoembolization (TACE), the mainstay treatment of unresectable primary liver cancer that primarily employs nondegradable drug-loaded embolic agents to achieve synergistic vascular embolization and locoregional chemotherapy effects, suffers from an inferior drug burst behavior lacking long-term drug release controllability that severely limits the TACE efficacy. Here we developed gelatin-based drug-eluting microembolics grafted with nanosized poly(acrylic acid) serving as a biodegradable ion-exchange platform that leverages a counterion condensation effect to achieve high-efficiency electrostatic drug loading with electropositive drugs such as doxorubicin (i.e., drug loading capacity >34 mg/mL, encapsulation efficiency >98%, and loading time <10 min) and an enzymatic surface-erosion degradation pattern (∼2 months) to offer sustained locoregional pharmacokinetics with long-lasting deep-tumor retention capability for TACE treatment. The microembolics demonstrated facile microcatheter deliverability in a healthy porcine liver embolization model, superior tumor-killing capacity in a rabbit VX2 liver cancer embolization model, and stabilized extravascular drug penetration depth (>3 mm for 3 months) in a rabbit ear embolization model. Importantly, the microembolics finally exhibited vessel remodeling-induced permanent embolization with minimal inflammation responses after complete degradation. Such a biodegradable ion-exchange drug carrier provides an effective and versatile strategy for enhancing long-term therapeutic responses of various local chemotherapy treatments.

Divalent ion partitioning through dense ion exchange membranes

Understanding the mechanism behind the permeation of multivalent ions through ion exchange membranes remains an ongoing challenge. Here we address this knowledge gap by presenting a molecular theory to elucidate the influence of counterion condensation and electrosteric effects on the (multivalent) divalent counterion permeation through such membranes. Building upon published experimental data (Galizia et al., 2017), we analyze the energetic tendencies of divalent counterions to associate with the fixed charge groups and their entropic preferences to disassociate to gain translational freedom, allowing us to quantitatively assess the partitioning of divalent ions at two distinct levels. (i) The global partitioning between the external 2:1 salt solution and the membrane, and (ii) the local partitioning within the interstitial solution and the crosslinked polymeric chains within the membrane. Notably, our observations reveal that the global partitioning of divalent counterions does not differ when the membranes operate separately in magnesium chloride (MgCl2) and calcium chloride (CaCl2) solutions. However, at the local partitioning level, we identify a higher preference for calcium counterions to associate with the fixed charge groups than magnesium ions. This preference arises from calcium ions’ more favorable charge density (physical size), facilitating their association/pairing with the fixed charge groups. The key takeaway message from this work is that when dealing with multivalent ions, we must downlevel our investigation, looking at how the counterions relax between the interstitial solution and the crosslinked polymeric chains and, in return, comprehending how it ultimately controls the global transport property of these membranes (such as their Donnan potential and water uptake).

Stretchable polyvinyl alcohol and sodium alginate double network ionic hydrogels for low-grade heat harvesting with ultrahigh thermopower

Recently, employing ionic thermoelectric (i-TE) materials is regarded as a promising strategy to harness low-grade waste heat due to their remarkable ionic Seebeck coefficient. By blending polyvinyl alcohol (PVA), sodium alginate (SA), and polyethylene glycol (PEG) and additional freeze-thaw method, PVA/SA/PEG hydrogel is developed. Via immersing the hydrogel in NaBF4 solutions with different concentrations, the TE and mechanical properties could be adjusted. PVA/SA/PEG/NaBF4-1.5 M hydrogel demonstrates exceptional mechanical properties, with tensile stress and strain up to 69 kPa and 114%, respectively. Moreover, PVA/SA/PEG/NaBF4-1.5 M hydrogel exhibits a high ionic conductivity of 31.4 mS/cm, a maximum ionic Seebeck coefficient of 66.7 mV/K, and an impressive power factor of 13.96 mW/m/K2. These outstanding performances originate from the synergistic effect of Manning's counterion condensation facilitated by SA and the crystal PVA chains. The prototype application of the PVA/SA/PEG/NaBF4-1.5 M hydrogel is demonstrated by a flexible ionic thermoelectric supercapacitor. With the external load resistance is 90 kΩ, the energy collected in one thermal cycle could achieve 4 mJ. This study introduces the exceptional stretchable PVA/SA/PEG/NaBF4 hydrogels with a record-high ionic Seebeck coefficient as promising i-TE materials for future TE application in low-grade waste heat.

Applying Copolymerization Kinetics to Understand and Optimize Swelling Responses in Superabsorbent Hydrogels

While acrylic acid (AA)-based superabsorbent hydrogels (SAHs) have been widely used in multiple applications, the effects of counterion condensation and the polyelectrolyte effect at suppressing the effective degree of ionization in such systems limit their superabsorbency. Herein we describe the use, and investigate the mechanism, of sulfate comonomers containing different types of polymerizable functional groups for increasing the superabsorbency of acrylic acid-based SAHs. Specifically, acrylamido-2-methylpropanesulfonic acid (AMPS), 3-sulfopropyl acrylate (SPAK), and 3-sulfopropyl methacrylate (SPMK) sulfated monomers featuring similar distances between the polymer backbone and the sulfate group but different polymerizable groups were copolymerized with acrylic acid to fabricate SAHs. Measurements of the effective homopolymerization rate constants and copolymerization ratios associated with each copolymerization enabled the prediction of the relative chain distributions of monomers in each copolymer, as quantified by the blockiness parameter (i.e., the instantaneous or average number of consecutive monomers of each type polymerized). While all sulfated comonomers significantly enhanced swelling relative to an acrylic acid control, copolymers in which longer AA blocks are produced (AA-AMPS) resulted in lower swelling than copolymers in which shorter AA blocks are produced (AA-SPAK, AA-SPMK), a result attributed to the suppressed polyelectrolyte effect in copolymers with shorter AA blocks. The formation of limited length blocks of the sulfated monomer SPMK showed additional benefits for enhancing swelling, consistent with enhanced direct charge–charge repulsion between fixed charges in such copolymer systems. We anticipate this linkage between copolymerization kinetics and swelling properties offers the potential to enable improved rational design of superabsorbent hydrogels with higher sorbency.

Shape control of deformable charge-patterned nanoparticles.

Deformable nanoparticles (NPs) offer unprecedented opportunities as dynamic building blocks that can spontaneously reconfigure during assembly in response to environmental cues. Designing reconfigurable materials based on deformable NPs hinges on an understanding of the shapes that can be engineered in these NPs. We solve for the low-energy shapes of charge-patterned deformable NPs by using molecular dynamics-based simulated annealing to minimize a coarse-grained model Hamiltonian characterized with NP elastic and electrostatic energies subject to a volume constraint. We show that deformable spherical NPs of radius 50nm whose surface is tailored with octahedrally distributed charged patches and double-cap charged patches adapt their shape differently in response to changes in surface charge coverage and ionic strength. We find shape transitions to rounded octahedra, faceted octahedra, faceted bowls, oblate spheroids, spherocylinders, dented beans, and dimpled rounded bowls. We demonstrate that similar shape transitions can be achieved in deformable NPs of different sizes. The effects of counterion condensation on the free-energetic drive associated with the observed deformations are examined via Manning model calculations that utilize simulation-derived estimates for the NP Coulomb energy under salt-free conditions. The charge-pattern-based shape control of deformable NPs has implications for the design of responsive nanocontainers and for assembling reconfigurable materials whose functionality hinges on the shape-shifting properties of their nanoscale building blocks.

Electrokinetic and dielectric response of a concentrated salt-free colloid: Different approaches to counterion finite-size effects.

In the present work, a general model is developed for the electrokinetics and dielectric response of a concentrated salt-free colloid that takes into account the finite size of the counterions released by the particles to the solution. The effects associated with the counterion finite size have been addressed using a hard-sphere model approach elaborated by Carnahan and Starling [N. F. Carnahan and K. E. Starling, Equationof state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969)0021-960610.1063/1.1672048]. A more simple description of the finite size of the counterions based on that by Bikerman has also been considered for comparison. The studies carried out in this work include predictions on the effect of the finite counterion size on the equilibrium properties of the colloid and its electrokinetic and dielectric response when it is subjected to constant or alternating electric fields. The results show how important the counterion finite-size effects are for most of the electrokinetic and dielectric properties of highly charged and concentrated colloids, mainly for the static and dynamic electrophoretic mobilities. Furthermore, new insights are provided on the counterion condensation effect when counterions are allowed to have finite size. Focus is placed on the changes undergone by their concentration in the condensation layer for low-salt and highly charged colloids.

Non-swellability of polyelectrolyte gel in divalent salt solution due to aggregation formation

The swelling behavior of polyelectrolyte gels depends on their ambient conditions owing to the ionic pressure of the Gibbs‒Donnan equilibrium. In a polyelectrolyte gel with a high fixed ion density, the counterion condensation effect influences the Gibbs‒Donnan equilibrium. In particular, the mechanism of the divalent salt effect remains unclear due to its complexity. This study investigated the swelling properties of polyelectrolyte gels in a divalent CaCl 2 salt solution using model polyelectrolyte gels called tetra-polyacrylic acid-polyethylene glycol gels (Tetra-PAA-PEG gels). In [Ca 2+ ] < 0.1 mM, the swelling ratios increased with increasing pH. With increasing Ca 2+ ions concentration, the gel showed the non-swellability independent of pH, which cannot be described by the simple mean-field theories. The viscoelastic and small-angle X-ray scattering measurements indicate that an aggregation formation due to the divalent salt induces an anomaly even in the model system. These findings will help understand the swelling behavior of polyelectrolyte gels in divalent salt systems. • Design of a model polyelectrolyte gel with alternating neutral and charged sequences. • Non-swellability was achieved in divalent salt solution even using the model system. • Well-disperse sphere structures were constructed by divalent salt. • Divalent salt-induced structural change resulting into non-swellability.

Effect of Nonlinear Elasticity on the Swelling Behaviors of Highly Swollen Polyelectrolyte Gels.

Polyelectrolyte gels exhibit swelling behaviors that are dependent on the external environment. The swelling behaviors of highly charged polyelectrolyte gels can be well explained using the Flory–Rehner model combined with the Gibbs–Donnan effect and Manning’s counterion condensation effect (the FRGDM model). This study investigated the swelling properties of a series of model polyelectrolyte gels, namely tetra-polyacrylic acid-polyethylene glycol gels (Tetra-PAA-PEG gels), and determined the applicability of the FRGDM model. The swelling ratio (Vs/V0) was well reproduced by the FRGDM model in the moderate swelling regime (Vs/V0 < 10). However, in the high swelling regime (Vs/V0 > 10), the FRGDM model is approx. 1.6 times larger than the experimental results. When we introduced the finite extensibility to the elastic free energy in the FRGDM model, the swelling behavior was successfully reproduced even in the high swelling regime. Our results reveal that finite extensibility is one of the factors determining the swelling equilibrium of highly charged polyelectrolyte gels. The modified FRGDM model reproduces well the swelling behavior of a wide range of polyelectrolyte gels.

Diffusiophoresis of a Highly Charged Soft Particle in Electrolyte Solutions.

Diffusiophoresis of a soft particle suspended in an infinite medium of symmetric binary electrolyte solution is investigated theoretically in this study, focusing on the chemiphoresis component when there is no global diffusion potential in the bulk solution. The general governing electrokinetic equations are solved with a pseudo-spectral method based on Chebyshev polynomials, and particle mobility, defined as the particle velocity per unit concentration gradient, is calculated. Parameters of electrokinetic interest are examined, in general, to explore their respective impact upon particle motion, such as the fixed charge density and permeability in the outer porous layer, the surface charge density and size of the inner rigid core, and the electrolyte strength in the solution. Nonlinear phenomena such as the motion-deterring double-layer polarization and the counterion condensation effects are scrutinized, in particular, for highly charged soft particles. Mobility reversal is observed in some range of electrolyte strength for highly charged particles. The generation of an axisymmetric counterclockwise vortex flow across the porous layer is found to be responsible for it. The onset of the mobility reversal is synchronized with the appearance or disappearance of this vortex flow. Mobility reversal may happen more than once, with particle moving toward or away from the region of higher solute concentration. The latter is undesirable in the application of drug delivery and thus should be avoided by delicate control of the electrokinetic environment. A local micro diffusion potential is discovered, which always speeds up the migration of coions and slows down that of counterions to guarantee that there is no net electric current across the double layer. Moreover, multilayer structure of the double-layer polarization is discovered when the electrolyte strength is high. The study presented here provides insight and crucial information for practical applications of soft particles, such as drug delivery.

Diffusiophoresis of a highly charged soft particle in electrolyte solutions induced by diffusion potential

Diffusiophoresis of a single soft particle in an electrolyte solution with induced diffusion potential is investigated theoretically in this study. A pseudo-spectral method based on Chebyshev polynomials is adopted to solve the resultant governing electrokinetic equations. Parameters of electrokinetic interest are examined extensively to explore their respective effect upon the particle motion, such as the fixed charge density and the permeability of the outer porous layer, the surface potential and size of the inner rigid core, and the electrolyte strength and magnitude of the induced diffusion potential in the solution. The nonlinear effects pertinent to highly charged particles, such as the double layer polarization effect and the counterion condensation effect, are scrutinized, in particular. Here, nonlinear effects refer to the effects that can only be properly revealed by accurately solving the complete nonlinear Poisson–Boltzmann equation governing the electric potential instead of the simplified linear Helmholtz equation under the Debye–Hückel approximation, valid for lowly charged particles only. We found, among other things, that characteristic local extrema in mobility profiles are mainly due to these two effects. Moreover, a soft particle moves fastest in dilute electrolyte solutions, in general. The smaller the soft particle is, the faster it moves under otherwise identical structural and electrokinetic conditions, provided that the particle radius is smaller than the Debye length, the characteristic thickness of the double layer. The shape of the double layer polarization takes an undulating multilayer form at large electrolyte strength. The results provided here are useful in practical applications such as drug delivery as well as microfluidic and nanofluidic operations.

Electrokinetic flow and electric conduction of salt-free solutions in a capillary.

The electrokinetic flow and accompanied electric conduction of a salt-free solution in the axial direction of a charged circular capillary are analyzed. No assumptions are made about the surface charge density (or surface potential) and electrokinetic radius of the capillary, which are interrelated. The Poisson-Boltzmann equation and modified Navier-Stokes equation are solved for the electrostatic potential distribution and fluid velocity profile, respectively. Closed-form formulas for the electroosmotic mobility and electric conductivity in the capillary are derived in terms of the surface charge density. The relative surface potential, electroosmotic mobility, and electric conductivity are monotonic increasing functions of the surface charge density and electrokinetic radius. However, the rises of the relative surface potential and electroosmotic mobility with an increase in the surface charge density are suppressed substantially when it is high due to the effect of counterion condensation. The analytical prediction that the electroosmotic mobility grows with increases in the surface charge density and electrokinetic radius agrees with the experimental results for salt-free solutions in circular microchannels in the literature.

Electrokinetic Flow of Salt-Free Solutions in a Fibrous Porous Medium.

The electrokinetic flow of a salt-free solution in the fibrous porous medium constituted by an array of parallel charged circular cylinders subject to a pressure gradient and an electric field imposed in the axial direction is analytically studied via the use of a unit cell model. The Poisson-Boltzmann equation and modified Navier-Stokes equation applicable to a unit cell accommodating the salt-free solution around an individual cylinder are solved to determine the electric potential profile and fluid velocity distribution. Results of the electroosmotic velocity and effective electric conductivity in the fiber matrix are obtained as functions of the surface charge density of the dielectric cylinders and the porosity of the fiber matrix. The effects of the porosity or interactions among the cylinders on the electric potential distribution, electroosmotic velocity, and effective electric conductivity are significant and interesting under practical conditions. The apparent zeta potential, electroosmotic velocity, and effective electric conductivity increase monotonically with an increase in the surface charge density of the cylinders. When the porosity of the fiber matrix and surface charge density of the cylinders are high, the increases of the apparent zeta potential and electroosmotic velocity with the surface charge density are substantially suppressed due to the counterion condensation effect. However, this effect becomes weak when the porosity is low.

The effect of chain stiffness and salt on the elastic response of a polyelectrolyte.

We present simulations of the force-extension curves of strong polyelectrolytes with varying intrinsic stiffness as well as specifically treating hyaluronic acid, a polyelectrolyte of intermediate stiffness. Whereas fully flexible polyelectrolytes show a high-force regime where extension increases nearly logarithmically with force, we find that the addition of even a small amount of stiffness alters the short-range structure and removes this logarithmic elastic regime. This further confirms that the logarithmic regime is a consequence of the short-ranged "wrinkles" in the flexible chain. As the stiffness increases, the force-extension curves tend toward and reach the wormlike chain behavior. Using the screened Coulomb potential and a simple bead-spring model, the simulations are able to reproduce the hyaluronic acid experimental force-extension curves for salt concentrations ranging from 1 to 500 mM. Furthermore, the simulation data can be scaled to a universal curve like the experimental data. The scaling analysis is consistent with the interpretation that, in the low-salt limit, the hyaluronic acid chain stiffness scales with salt with an exponent of -0.7, rather than either of the two main theoretical predictions of -0.5 and -1. Furthermore, given the conditions of the simulation, we conclude that this exponent value is not due to counterion condensation effects, as had previously been suggested.

PHYSICAL-CHEMICAL PROPERTIES OF CHONDROITIN SULFATE IN AGGRECAN

In current work theoretical study of physical-chemical properties of chondroitin sulfate in aggrecan within the self-consistent field theory was developed. As a model for aggrecan a model of cylindrical polymer brush was chosen. Aggrecan is considered as a system of n gaussian polymer chains consisting of N segments tethered to cylindrical surface of core protein. Basing on the results of previous work where using gaussian equivalent representation for functional integrals equation of state for chondroitin sulfate in aqueous solution was obtained and also osmotic pressure, dissociation degree, radius of gyration and renormalized persistent length were calculated with respect to monomers electrostatic interactions and effect of counterion condensation, one can obtain configuration integral for cylindrical polymer brush. Persistent length is introduced instead of Kuhn segment length which supposedly helps one to take into account rigidity of polymer chain determined by electrostatic repulsion of monomers (disaccharides groups). Expression for free energy of a polymer brush modeled as chondroitin sulfate chains tethered to a cylindrical surface was obtained. Dependence of chondroitin sulfate in aggrecan dissociation degree as a function of distance from the cylindrical surface is represented. For given system it varies insignificantly from the one for free chains in solution. Results for a polymer density as a function of distance from the cylindrical surface obtained within mean-field approximation are in qualitative agreement with those obtained using density functional method. However, calculations within a mean field framework are understable, thus it is necessary to use regularization methods.Forcitation:NogovitsynE.A., KalikinN.N., ZheleznyakN.I. Physical-chemical properties of chondroitin sulfate in aggrecan. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2018. V. 61. N 2. P. 35-39

Response to Alternating Electric Fields of Tubulin Dimers and Microtubule Ensembles in Electrolytic Solutions

Microtubules (MTs), which are cylindrical protein filaments that play crucial roles in eukaryotic cell functions, have been implicated in electrical signalling as biological nanowires. We report on the small-signal AC (“alternating current”) conductance of electrolytic solutions containing MTs and tubulin dimers, using a microelectrode system. We find that MTs (212 nM tubulin) in a 20-fold diluted BRB80 electrolyte increase solution conductance by 23% at 100 kHz, and this effect is directly proportional to the concentration of MTs in solution. The frequency response of MT-containing electrolytes exhibits a concentration-independent peak in the conductance spectrum at 111 kHz (503 kHz FWHM that decreases linearly with MT concentration), which appears to be an intrinsic property of MT ensembles in aqueous environments. Conversely, tubulin dimers (42 nM) decrease solution conductance by 5% at 100 kHz under similar conditions. We attribute these effects primarily to changes in the mobility of ionic species due to counter-ion condensation effects, and changes in the solvent structure and solvation dynamics. These results provide insight into MTs’ ability to modulate the conductance of aqueous electrolytes, which in turn, has significant implications for biological information processing, especially in neurons, and for intracellular electrical communication in general.

Bending stiff charged polymers: The electrostatic persistence length

Many charged polymers, including nucleic acids, are locally stiff. Their bending rigidity —quantified by the persistence length— depends crucially on Coulombic features, such as the ionic strength of the solution which offers a convenient experimental route for tuning the rigidity. While the classic Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple analytical formula for the electrostatic persistence length. It is shown to be in remarkable agreement with numerically obtained Poisson-Boltzmann theory results, thereby fully accounting for non-linearities, among which counter-ion condensation effects. Specified to double-stranded DNA, our work reveals that the widely used bare persistence length of 500 Å is overestimated by some 20%.

Design of Nanoporous Carbons as Anode Materials for Sodium (Na) Ion Batteries

Molecular dynamics simulations have been employed to study the structural properties of non-aqueous (organic) electrolyte solutions confined within carbon nanopores. The effects of pore size and surface charge density were quantified by calculating ionic density profiles and concentration within the pores. Graphene slit pores of widths 0.72-10 nm were considered. The graphene surfaces were charged with densities ranging from 0 (neutral pores), -0.8e/nm2 , -1.2e/nm2 , -2e/nm2. As the surface charge density increases, more Na+ ions enter the pores. When the graphene surface is highly charged the Na+ ions are adsorbed due to counterion condensation effect.

Ionic Effects on VEGF G-Quadruplex Stability.

In a potassium solution, a modified 22-meric DNA sequence Pu22-T12T13 from a region proximal to the transcription initiation site of the human VEGF gene adopts a single parallel-stranded G-quadruplex conformation with a 1:4:1 loop-size arrangement. We measured the thermal stability, TM, of the K(+)-stabilized Pu22-T12T13 G-quadruplex as a function of stabilizing K(+) ions and nonstabilizing Cs(+) and TMA(+) ions. The thermal stability, TM, of the Pu22-T12T13 G-quadruplex increases with the concentration of the stabilizing potassium ions, while it sharply decreases upon the addition of the nonstabilizing cations. We interpret these results as underscoring the opposing effects of internal binding and counterion condensation on the stability of the Pu22-T12T13 G-quadruplex. While centrally bound ions stabilize the G-quadruplex conformation, counterion condensation destabilizes it, favoring the coil conformation. From the initial slopes of the dependences of TM on the concentration of Cs(+) and TMA(+) cations, we estimate that the deleterious effect of counterion condensation stems from roughly one extra counterion associated with the coil relative to the G-quadruplex state of Pu22-T12T13. The reduced accumulation of counterions around the G-quadruplex state of Pu22-T12T13 relative to its coil state is due to the low surface charge density of the G-quadruplex reflecting its structural characteristics. On the basis of the analysis of our data along with the results of a previous study, we propose that the differential effect of internally (stabilizing) and externally (destabilizing) bound cations may be a general feature of parallel intramolecular G-quadruplexes.

Isotropic–nematic transition and dynamics of rigid charged molecules

Using molecular dynamics, an isotropic–nematic transition was found in bulk salt-free solutions of charged rods with their counterions in the semidilute regime. This phase transition is driven primarily by electrostatics, rather than by excluded volume. The counterion condensation effect, which is controlled by the Manning parameter, leads to liquid crystalline phases of rods. For elevated values of the Manning parameter, an attraction is obtained between the rods, and the nematic phase appears. For small values of the Manning parameter the counterions de-condense, and the nematic phase disappears. Instead, in a neutral system of rods and spheres there is no appearance of nematic phase. The diffusivity of both rods and counterions is reduced with the Manning parameter.