Monovalent Counterions Research Articles

Adsorption of polyelectrolytes in the presence of varying dielectric discontinuity between solution and substrate.

We examine the interactions between polyelectrolytes (PEs) and uncharged substrates under conditions corresponding to a dielectric discontinuity between the aqueous solution and the substrate. To this end, we vary the relevant system characteristics, in particular the substrate dielectric constant ɛs under different salt conditions. We employ coarse-grained molecular dynamics simulations with rodlike PEs in salt solutions with explicit ions and implicit water solvent with dielectric constant ɛw = 80. As expected, at low salt concentrations, PEs are repelled from the substrates with ɛs < ɛw but are attracted to substrates with a high dielectric constant due to image charges. This attraction considerably weakens for high salt and multivalent counterions due to enhanced screening. Furthermore, for monovalent salt, screening enhances adsorption for weakly charged PEs, but weakens it for strongly charged ones. Meanwhile, multivalent counterions have little effect on weakly charged PEs, but prevent adsorption of highly charged PEs, even at low salt concentrations. We also find that correlation-induced charge inversion of a PE is enhanced close to the low dielectric constant substrates, but suppressed when the dielectric constant is high. To explore the possibility of a PE monolayer formation, we examine the interaction of a pair of like-charged PEs aligned parallel to a high dielectric constant substrate with ɛs = 8000. Our main conclusion is that monolayer formation is possible only for weakly charged PEs at high salt concentrations of both monovalent and multivalent counterions. Finally, we also consider the energetics of a PE approaching the substrate perpendicular to it, in analogy to polymer translocation. Our results highlight the complex interplay between electrostatic and steric interactions and contribute to a deeper understanding of PE-substrate interactions and adsorption at substrate interfaces with varying dielectric discontinuities from solution, ubiquitous in biointerfaces, PE coating applications, and designing adsorption setups.

Effect of charge inversion on the electrokinetic transport of nanoconfined multivalent ionic solutions

Understanding the effects of phenomena occurring at electrically charged interfaces, such as charge inversion (CI), is crucial for enabling electroosmosis as an efficient transport mechanism in nanodevices. Here, we employ molecular dynamics (MD) simulations to systematically analyze the effect of CI on the electrokinetic transport of multivalent ionic solutions confined in amorphous silica nanochannels. We employ mixtures of monovalent and multivalent counterions while fixing the total ionic concentration to establish correlations between observed phenomena and the amount of multivalent ionic species in the electrolyte solution. The results show that the development of CI is related to a decrease in the mobility of the fluid layers adjacent to the charged surface. In addition, we observe that interfacial overcharging disrupts the water molecular orientation in the fluid layers adjacent to the channel walls. From the non-equilibrium MD simulations of electro-osmotic flow, we disclose the influence of phenomena related to the presence of CI. In particular, flow reversal occurs in scenarios involving CI due to increased local viscosity and a higher concentration of coions within the hydrodynamically mobile and electrokinetically active region of the charged interface. We also find that the magnitude of the wall zeta (ζ) potential displays a monotonic increase with the development of CI in the system. Moreover, we explain why positioning the wall ζ potential at an imaginary (slip) plane, which separates the hydrodynamically mobile and immobile fluid, is misleading.

Selective divalent/monovalent ion partitioning in cation exchange membranes

The selective partitioning of divalent and monovalent counterions through cation exchange membranes immersed in 2:1 and 1:1 binary salt solutions remains unclear, especially at the molecular level. We present a theoretical framework that quantifies these membranes’ sorption of divalent and monovalent ions, incorporating condensed and free variants to reconcile deviations from the ideal Donnan picture observed in published experimental data. This framework explores the membranes’ global and local selective ion sorption characteristics by assessing the effects of competitive ion condensations, where these counterions compete to bind to the fixed charge groups. First, we calculate the thermodynamic property—the global partition ratio—of the membranes immersed in these binary salt solutions, quantifying the partitioning between the binary salt solutions and the membranes. Our theoretical results successfully capture the published experimental partitioning data for membranes immersed in equimolar and non-equimolar 2:1 and 1:1 binary salt solutions. Furthermore, the Donnan potential of the membranes reciprocally changes with the total concentration of 2:1 and 1:1 external salt solutions. However, for the non-equimolar systems at a constant low total concentration, varying the binary solution concentration ratio of 2:1 to 1:1 salts maintains a strong electric potential intensity due to high ionic imbalance. Second, we quantify the local partitioning of the sorbed counterions that are condensed on the crosslinked polymeric chains and those that are mobile in the interstitial solution of the membrane, a variable that is difficult to access experimentally. Accordingly, we can fractionate the sorbed ions into condensed and free states, which mutually govern the membrane’s kinetic and thermodynamic (global and local partitioning) properties.

Implicit Solvent with Explicit Ions Generalized Born Model in Molecular Dynamics: Application to DNA.

The ion atmosphere surrounding highly charged biomolecules, such as nucleic acids, is crucial for their dynamics, structure, and interactions. Here, we develop an approach for the explicit treatment of ions within an implicit solvent framework suitable for atomistic simulations of biomolecules. The proposed implicit solvent/explicit ions model, GBION, is based on a modified generalized Born (GB) model; it includes separate, modified GB terms for solute-ion and ion-ion interactions. The model is implemented in the AMBER package (version 24), and its performance is thoroughly investigated in atomistic molecular dynamics (MD) simulations of double-stranded DNA on a microsecond time scale. The aggregate characteristics of monovalent (Na+ and K+) and trivalent (Cobalt Hexammine, CoHex3+) counterion distributions around double-stranded DNA predicted by the model are in reasonable agreement with the experiment (where available), all-atom explicit water MD simulations, and the expectation from the Manning condensation theory. The radial distributions of monovalent cations around DNA are reasonably close to the ones obtained using the explicit water model: expressed in units of energy, the maximum deviations of local ion concentrations from the explicit solvent reference are within 1 kBT, comparable to the corresponding deviations expected between different established explicit water models. The proposed GBION model is able to simulate DNA fragments in a large volume of solvent with explicit ions with little additional computational overhead compared with the fully implicit GB treatment of ions. Ions simulated using the developed model explore conformational space at least 2 orders of magnitude faster than in the explicit solvent. These advantages allowed us to observe and explore an unexpected "stacking" mode of DNA condensation in the presence of trivalent counterions (CoHex3+) that was revealed by recent experiments.

A Two-Step Intermolecular Interaction Of Molecular Macroions With Multivalent Counterions.

Macroion-counterion interaction is essential for regulating the solution behaviors of hydrophilic macroions, as simple models for polyelectrolytes. Here, we explore the interaction between uranyl peroxide molecular cluster Li68K12(OH)20[UO2(O2)OH]60 (U60) and multivalent counterions. Different from interaction with monovalent counterions that shows a simple one-step process, isothermal titration calorimetry, combined with light/X-ray scattering measurements and electron microscopy, confirm a two-step process for their interaction with multivalent counterions: an ion-pairing between U60 and the counterion with partial breakage of hydration shells followed by strong U60-U60 attraction, leading to the formation of large nanosheets with severe breakage and reconstruction of hydration shells. The detailed studies on macroion-counterion interaction can be nicely correlated to the microscopic (self-assembly) and macroscopic (gelation or phase separation) phase transitions in the dilute U60 aqueous solutions induced by multivalent counterions.

Ion-Specific Effects on Ion and Polyelectrolyte Solvation.

Ion-specific effects on aqueous solvation of monovalent counter ions, Na , K , Cl , and Br , and two model polyelectrolytes (PEs), poly(styrene sulfonate) (PSS) and poly(diallyldimethylammonium) (PDADMA) were here studied with ab initio molecular dynamics (AIMD) and classical molecular dynamics (MD) simulations based on the OPLS-aa force-field which is an empirical fixed point-charge force-field. Ion-specific binding to the PE charge groups was also characterized. Both computational methods predict similar response for the solvation of the PEs but differ notably in description of ion solvation. Notably, AIMD captures the experimentally observed differences in Cl and Br anion solvation and binding with the PEs, while the classical MD simulations fail to differentiate the ion species response. Furthermore, the findings show that combining AIMD with the computationally less costly classical MD simulations allows benefiting from both the increased accuracy and statistics reach.

Multi-component ion equilibria and transport in ion-exchange membranes

At the interface between an ion-exchange membrane and a multi-electrolyte solution, charged species redistribute themselves to minimize the free energy of the system. In this paper, we explore the Donnan equilibrium of membranes with quaternary electrolyte (Na+/Mg2+/K+/Ca2+/Cl−) solutions, experimentally. The data was used to calculate the ion activity coefficients for six commercial cation-exchange membranes (CEMs). After setting one of the activity coefficients to an arbitrary value, we used the remaining (N-1) activity coefficients as fitting parameters to describe the equilibrium concentrations of (N) ionic species with a mean relative error of 3 %. At increasing solution ionic strengths, the equivalent ion fractions of monovalent counter-ions inside the membrane increased at the expense of the multivalent ones in alignment with the Donnan equilibrium theory. The fitted activity coefficients were employed in a transport model that simulated a Donnan dialysis experiment involving all four cations simultaneously. The arbitrary value assigned to one activity coefficient affects the calculated Donnan potential at the membrane interface. Nevertheless, this arbitrary value does not affect the prediction of the ion concentrations inside the membrane and consequently does not affect the modeled ion fluxes.

Effect of Counterions on the Soft Ionization Mass Spectra of Analytes with Multiple Permanent Charges.

Multiply permanently charged analytes (MPCAs) are of great interest for various applications. MPCA soft ionization mass spectra (MS) strongly depend on the counterions of MPCA. We have studied thoroughly this effect to expand the use of MS in MPCA characterization. To this end, β-cyclodextrin-based MPCAs with 7 (MIM7NBCD) and 14 (MIM14BCD) quaternary ammonium charges with a series of monovalent counterions were prepared and their MS were measured using two of the most popular soft ionization techniques, electrospray ionization (ESI) and matrix-assisted laser desorption ionization (MALDI). MALDI MS of both analytes were well resolved, with signals assignable to the analytes only with the two least basic tested counterions (ClO4- and TfO-). Similarly, analyte-assignable signals were observed in ESI MS of MIM14BCD only with ClO4- and TfO-. The situation was opposite with ESI MS of MIM7NBCD where assignable signals were observed with Cl- but not with TfO-. Thus, to get high-quality MS, binding between the MPCA permanent charges and the counterions must be of the optimal effective strength, given also by the number of analyte permanent charges as shown by the simple combinatorial model of binding. Of practical interest is the observation that unsuitable counterions can be replaced in situ by an excess of corresponding acid. The findings form a coherent framework for interpreting and improving MPCA mass spectra.

Mobility of Condensed Counterions in Ion-Exchange Membranes: Application of Screening Length Scaling Relationship in Highly Charged Environments.

Ion-exchange membranes (IEMs) are widely used in water, energy, and environmental applications, but transport models to accurately simulate ion permeation are currently lacking. This study presents a theoretical framework to predict ionic conductivity of IEMs by introducing an analytical model for condensed counterion mobility to the Donnan-Manning model. Modeling of condensed counterion mobility is enabled by the novel utilization of a scaling relationship to describe screening lengths in the densely charged IEM matrices, which overcame the obstacle of traditional electrolyte chemistry theories breaking down at very high ionic strength environments. Ionic conductivities of commercial IEMs were experimentally characterized in different electrolyte solutions containing a range of mono-, di-, and trivalent counterions. Because the current Donnan-Manning model neglects the mobility of condensed counterions, it is inadequate for modeling ion transport and significantly underestimated membrane conductivities (by up to ≈5× difference between observed and modeled values). Using the new model to account for condensed counterion mobilities substantially improved the accuracy of predicting IEM conductivities in monovalent counterions (to as small as within 7% of experimental values), without any adjustable parameters. Further adjusting the power law exponent of the screen length scaling relationship yielded reasonable precision for membrane conductivities in multivalent counterions. Analysis reveals that counterions are significantly more mobile in the condensed phase than in the uncondensed phase because electrostatic interactions accelerate condensed counterions but retard uncondensed counterions. Condensed counterions still have lower mobilities than ions in bulk solutions due to impedance from spatial effects. The transport framework presented here can model ion migration a priori with adequate accuracy. The findings provide insights into the underlying phenomena governing ion transport in IEMs to facilitate the rational development of more selective membranes.

The conformational phase diagram of charged polymers in the presence of attractive bridging crowders.

Using extensive molecular dynamics simulations, we obtain the conformational phase diagram of a charged polymer in the presence of oppositely charged counterions and neutral attractive crowders for monovalent, divalent, and trivalent counterion valencies. We demonstrate that the charged polymer can exist in three phases: (1) an extended phase for low charge densities and weak polymer-crowder attractive interactions [Charged Extended (CE)]; (2) a collapsed phase for high charge densities and weak polymer-crowder attractive interactions, primarily driven by counterion condensation [Charged Collapsed due to Intra-polymer interactions [(CCI)]; and (3) a collapsed phase for strong polymer-crowder attractive interactions, irrespective of the charge density, driven by crowders acting as bridges or cross-links [Charged Collapsed due to Bridging interactions [(CCB)]. Importantly, simulations reveal that the interaction with crowders can induce collapse, despite the presence of strong repulsive electrostatic interactions, and can replace condensed counterions to facilitate a direct transition from the CCI and CE phases to the CCB phase.

Cluster Formation in Solutions of Polyelectrolyte Rings.

We use molecular dynamics simulations to explore concentrated solutions of semiflexible polyelectrolyte ring polymers, akin to the DNA mini-circles, with counterions of different valences. We find that the assembly of rings into nanoscopic cylindrical stacks is a generic feature of the systems, but the morphology and dynamics of such a cluster can be steered by the counterion conditions. In general, a small addition of trivalent ions can stabilize the emergence of clusters due to the counterion condensation, which mitigates the repulsion between the like-charged rings. Stoichiometric addition of trivalent ions can even lead to phase separation of the polyelectrolyte ring phase due to the ion-bridging effects promoting otherwise entropically driven clustering. On the other hand, monovalent counterions cause the formation of stacks to be re-entrant with density. The clusters are stable within a certain window of concentration, while above the window the polyelectrolytes undergo an osmotic collapse, disfavoring ordering. The cluster phase exhibits characteristic cluster glass dynamics with arrest of collective degrees of freedom but not the self-ones. On the other hand, the collapsed phase shows arrest on both the collective and single level, suggesting an incipient glass-to-glass transition, from a cluster glass of ring clusters to a simple glass of rings.

Tuning Structure and Rheological Properties of Polyelectrolyte-Based Hydrogels through Counterion-Specific Effects

Tuning at will the properties of gel-forming systems is of key relevance for many biotechnological, agricultural, and biomedical applications. For polyelectrolyte-based gels, ion-specific effects can be an attractive way for this purpose. This study investigates the counterion-specific effect on the microscopic structure and the rheological properties of a physical hydrogel formed of ionene-type cationic polyelectrolytes. The focus is on two monovalent halide counterions (F– and Cl–) and a divalent counterion (SO42–). A strong counterion-specific effect appears within ionene-based gels. In the case of halide counterions, gelation is more effective for more weakly hydrated counterions. Indeed, strongly hydrated counterions maintain electrostatic repulsions between the chains and as a consequence gel formation is shifted toward higher concentrations (higher critical gelation concentration, CGC). The combination of the complementary small-angle X-ray and neutron scattering (SAXS and SANS) techniques reveals a strong contribution of ion–ion correlations in the structure of the gel network. Contrary to chloride gels, which present a single correlation length characterizing the distance between the cross-linking nodes, fluoride gels present an additional network of nodes. This is accompanied by a very rapid increase of the elastic modulus of fluoride gels, once CGC is reached. With divalent counterions, the gelation is even more remarkable with a lower CGC and a higher elastic modulus at equivalent polyelectrolyte concentrations. The presence of divalent counterions favors the association of chains, probably by a bridging effect. This evokes the “egg-box” model, and the characteristic scaling of the elastic modulus with reduced gel concentration confirms this. However, only a narrow concentration window for gel-forming exists for divalent counterions before precipitation takes over due to too strong attractive chain–chain interactions.

Ion-induced changes in DNA gels.

Small angle neutron scattering (SANS) measurements are reported for DNA gels under near physiological conditions in which the concentration of monovalent and divalent counter-ions and the pH are varied. The scattering intensity I(q) is described by a two-term equation, one due to osmotic concentration fluctuations and the other coming from static inhomogeneities frozen in by the cross-links. SANS in the low q range indicates the presence of large clusters and the size of which exceeds the resolution of the experiment. In the intermediate q-range, the intensity increases with the CaCl2 concentration and the slope approaches -1, corresponding to linear (rod-like) scatterers. In the highest q region, the scattering response is governed by the local chain geometry. Screening of electrostatic interactions by sodium chloride causes a moderate increase in the SANS intensity that is accompanied by an increase in the mesh size L of the network. Addition of calcium chloride, or a decrease in pH, produces similar trends, and ultimately leads to phase separation. The scattering intensity at q = 0, estimated from independent measurements of the osmotic pressure Π, is in excellent agreement with I(0) from the SANS measurements. Anomalous small angle X-ray scattering (ASAXS) measurements on the uncross-linked DNA show that the monovalent ion cloud is only weakly influenced by the addition of divalent ions. Conversely, the divalent counter-ion cloud tightly follows the contour of polymer chains.

Measurement and Correlation of Solubility of L–Tryptophan in Aqueous Solutions with a Wide Range of pH and Different Monovalent Counterions from 283.15 to 323.15 K

Measurement and Correlation of Solubility of L–Tryptophan in Aqueous Solutions with a Wide Range of pH and Different Monovalent Counterions from 283.15 to 323.15 K

Impact of counterion valency on the rheology of sulfonated cellulose nanocrystal hydrogels

A systematic rheological study on the influence of valency of different counterions on the properties of CNC hydrogels was carried out. Rheo-polarized microscopy was used to prove that preshear of 500 s−1 for 1 min is adequate to completely breakdown agglomerates in the suspension. Furthermore, a rest period of 30 min is sufficient to recover the equilibrium structure of hydrogels. Changing counterions from monovalent (Na+, K+, Li+), to divalent (Mg2+, Ca2+) and to trivalent (Al3+) influenced the network formation. CNC suspensions with monovalent counterions are isotropic at 3 wt%, anisotropic with chiral nematic structures at 5 wt% and form birefringent gels at 7 wt%. Conversely, divalent and trivalent counterions facilitate network formation, leading to gel like behavior at all concentrations. Sonication of CNC samples with monovalent counterions lowers the viscosity by two orders of magnitude while the opposite is true for multivalent counterions due to the formation of strong networks. The varying rheological properties displayed from CNCs with different counter ions may influence the use of CNC as rheological modifiers in fluid-based applications.

Quantifying the coupled monovalent and divalent ions sorption in dense ion-exchange membranes

As a universal phenomenon in solution-membrane systems, the coupled competitive monovalent and divalent ions sorption significantly impacts the transport process in ion-exchange membranes. Often, the quantitative and qualitative relationships between them are unclear. Here, we present a lattice-based molecular model to capture the interplay effect of ion-pairing and electrostatic interaction on the competitive partitioning process. In particular, we utilize statistical mechanics to formulate how the monovalent and divalent counterions competitively pair with the fixed charge group in the membranes. To this end, the model can quantify (a) the counterions sorption and (b) the coion repulsion within the membranes, which, collectively, allow us to quantify the ion partitioning and the pairing site saturation. To showcase the capability of our model, we compare our results with published experiment data, where we achieve a relatively good agreement between them. We demonstrate that the competitive ion partitioning depends highly upon (i) the entropy change generated by the counterions pairing with the fixed charge group, (ii) the binding energy, and (iii) the osmotic pressure, and (iv) the electrostatic interaction. These different factors can explain the favorable sorption of divalent counterions in the cation-exchange membranes but monovalent counterions in the anion ones, as previously reported. Altogether, our theoretical approach provides an insight into the fundamental understanding of coupled competitive monovalent and divalent ions sorption within the dense ion-exchange membranes, further enhancing the knowledge of the competitive ion partitioning process.

Effects of Solid State Sulfonation of Poly(phenylene) on Mechanical Robustness and Proton Conductivity

To meet ever increasing demands for energy worldwide, advances in both energy storage and energy conversion must be meet. Fuel cells, especially polymer electrolyte fuel cells (PEMFCs), and vanadium redox batteries problems include electrolyte instability and fuel crossover. Nafion® is the industry standard, but several drawbacks include low selectivity due to it bicontinuous morphology, large water uptake, and production cost. Several alternative ionomers have been investigated, however post sulfonated diels alder poly(phenylene) membranes have shown ideal properties with respect to selectivity, mechanical robustness, ionic conductivity, and thermal transitions. A homogeneous sulfonation has limits due to swelling above an IEC of 2.2 This study focuses on a solid-state surface modification in dilute and sub-ambient conditions via direct immersion in a chlorosulfonic acid solution followed by an exchange with a monovalent counter-ion. Planned thermal and mechanical studies include defining degradation temperature, toughness, and Young’s modulus in the monovalent form. Further property determination includes assigning experimentally determined diffusion coefficients for water vapor, proton conductivity, gas, and liquid water. Both in plane and through plane conductivity measurements are planned to be done at different degrees of water saturation. Lastly, chemical composition and structure will be determined through Fourier transform infrared spectroscopy- attenuated total reflectance studies and transmission and grazing-incidence small-angle x-ray scattering. Future studies include evaluation of fuel cell performance and further phase analysis through transmission electron microscopy.

Gelation behavior and mechanism of alginate with calcium: Dependence on monovalent counterions

The present work investigates the calcium-induced gelation behavior and gel properties of alginate samples of lithium-, sodium-, and potassium-forms. It was found that the effect of the alkali metal counterions varied greatly with the calcium concentration regime, namely, the molar ratio of calcium to guluronate (R = Ca/G). Four different regions were identified, including R < 0.25, 0.25 < R < 0.55, 0.55 < R < 1.0, and R > 1.0. The counterion dependence was interpreted by the relative interaction strength of the monovalent cations with COO− groups and their exchange reaction with Ca2+ ions. A mechanistic model depicting the role of counterions was proposed in relation to different steps of the binding and gelation of alginate with calcium. The knowledge gained in the study would further advance the understanding of the gelation mechanism of the industrially important alginate and guide its specific utilizations.

Interaction between surfaces decorated with like-charged pendants: Unravelling the interplay between energy and entropy leading to attraction

HypothesisThe stronger motional coupling between monovalent counterions neutralizing homogeneously like-charged surfaces induced by an increase in charge density is known to foster inter–surface attraction. Compared to a uniformly distributed charge, point-like charges generate locally more intense fields, so that the correlation induced between counterions may be even stronger despite an identical total charge. It should thus be possible to induce surface attraction at lower charge densities than commonly expected. ExperimentsMonte Carlo simulations on primitive electrolyte models have been exploited to compute potential of mean force profiles and mobile ion densities for systems composed of two parallel surfaces bearing surface-tethered monovalent like-charged pendants as a function of the surface distance and pendant densities. FindingsSurfaces bearing like-charged pendants are found to attract each other over a wide range of distances despite the presence of very low charge densities. Notwithstanding the attractive contribution to the inter-surface forces provided by electrostatic interactions, the entropic component of the system Helmholtz energy is found to play the key role in defining the overall magnitude. The latter finding appears justified by an increase in the relative delocalization of counterions upon decreasing the surface distance.

Dielectric Manipulation of Polymer Translocation Dynamics in Engineered Membrane Nanopores.

The alteration of the dielectric membrane properties by membrane engineering techniques such as carbon nanotube (CNT) coating opens the way to novel molecular transport strategies for biosensing purposes. In this article, we predict a macromolecular transport mechanism enabling the dielectric manipulation of the polymer translocation dynamics in dielectric membrane pores confining mixed electrolytes. In the giant permittivity regime of these engineered membranes governed by attractive polarization forces, multivalent ions adsorbed by the membrane nanopore trigger a monovalent ion separation and set an electroosmotic counterion flow. The drag force exerted by this flow is sufficiently strong to suppress and invert the electrophoretic velocity of anionic polymers and also to generate the mobility of neutral polymers whose speed and direction can be solely adjusted by the charge and concentration of the added multivalent ions. These features identify the dielectrically generated transport mechanism as an efficient means to drive overall neutral or weakly charged analytes that cannot be controlled by an external voltage. We also reveal that, in anionic polymer translocation, multivalent cation addition into the monovalent salt solution amplifies the electric current signal by several factors. The signal amplification is caused by the electrostatic many-body interactions replacing the monovalent polymer counterions by the multivalent cations of higher electric mobility. The strength of this electrokinetic charge discrimination points out the potential of multivalent ions as current amplifiers capable of providing boosted resolution in nanopore-based biosensing techniques.