Multivalent Salt Solutions Research Articles

Anionic species from multivalent metal salts are differentially retained during aqueous ionic gelation of sodium alginate and could fine-tune the hydrogel properties

The role of anionic counterions of divalent metal salts in alginate gelation and hydrogel properties has been thoroughly investigated. Three anions were selected from the Hofmeister series, namely sulphate, acetate and chloride, paired in all permutations and combinations with divalent metal cations like calcium, zinc and copper. Spectroscopic analysis revealed the presence of anions and their interaction with the respective metal cations in the hydrogel. The data showed that the gelation time and other hydrogel properties were largely controlled by cations. However, subtle yet significant variations in viscoelasticity, water uptake, drug release and cytocompatibility properties were anion dependent in each cationic group. Computational modelling based study showed that metal-anion-alginate configurations were energetically more stable than the metal-alginate models. The in vitro and in silico studies concluded that acetate anions preceded chlorides in the drug release, swelling and cytocompatibility fronts, followed by sulphate anions in each cationic group. Overall, the data confirmed that anions are an integral part of the metal-alginate complex. Furthermore, anions offer a novel option to further fine-tune the properties of alginate hydrogels for myriads of applications. In addition, full exploration of this novel avenue would enhance the usability of alginate polymers in the pharmaceutical, environmental, biomedical and food industries.

Ion correlation-driven like-charge attraction in multivalent salt solutions.

The electrostatic double layer force is key to determining the stability and self-assembly of charged colloids and many other soft matter systems. Fully understanding the attractive force between two like-charged surfaces remains a great challenge. Here, we apply the modified Gaussian renormalized fluctuation theory to study ion correlation-driven like-charge attraction in multivalent salt solutions. The effects of spatially varying ion correlations on the structure of overlapping double layers and their free energy are self-consistently accounted for. In the presence of multivalent salts, increasing surface charge or counterion valency leads to a short-range attraction. We demonstrate that although both overcharging and like-charge attraction are outcomes of ion correlation, there is no causal relationship between them. Our theory also captures the non-monotonic dependence of like-charge attraction on multivalent salt concentration. The reduction of attraction at high salt concentrations could be a contributing factor toward the reentrant stability of charged colloidal suspensions. Our theoretical predictions are consistent with the observations reported in experiments and simulations.

Coion exclusion properties of cation exchange membranes in 2:1 divalent salt solutions

The selectivity of ion exchange membranes hinges on their capacity to exclude coions. Yet, understanding how they reject coions in multivalent salt solutions remains challenging. This study presents a new molecular theory to understand coion exclusion. It examines counterion and coion condensation, including electrosteric effects. Supported by experimental data [Gokturk et al., Nat. Commun., 13 (2022)], we analyze cation exchange membrane potential in a 2:1 salt solution, revealing insights into coion selectivity and exclusion mechanisms. Notably, our theory deviates from earlier research by accommodating condensed divalent counterions that bind to one or two fixed-charged monomers. Additionally, we account for many-body electrostatic interactions, allowing the former to bind to sorbed coions. Our findings highlight the importance of coion condensation, especially in low-concentration salt conditions where coions are mainly condensed. This effect becomes less significant as the external solution concentration rises. These findings clarify the suitability of the ideal Donnan model in high-concentration salts, but its accuracy decreases in low-concentration situations. To summarize, our study emphasizes the need to account for counterion and coion condensation to understand membrane selectivity in low-concentration multivalent salt solutions.

Theoretical and computational analysis of the electrophoretic polymer mobility inversion induced by charge correlations.

Electrophoretic (EP) mobility reversal is commonly observed for strongly charged macromolecules in multivalent salt solutions. This curious effect takes place, e.g., when a charged polymer, such as DNA, adsorbs excess counterions so that the counterion-dressed surface charge reverses its sign, leading to the inversion of the polymer drift driven by an external electric field. In order to characterize this seemingly counterintuitive phenomenon that cannot be captured by electrostatic mean-field theories, we adapt here a previously developed strong-coupling-dressed Poisson-Boltzmann approach to the cylindrical geometry of the polyelectrolyte-salt system. Within the framework of this formalism, we derive an analytical polymer mobility formula dressed by charge correlations. In qualitative agreement with polymer transport experiments, this mobility formula predicts that the increment of the monovalent salt, the decrease of the multivalent counterion valency, and the increase of the dielectric permittivity of the background solvent suppress charge correlations and increase the multivalent bulk counterion concentration required for EP mobility reversal. These results are corroborated by coarse-grained molecular dynamics simulations showing how multivalent counterions induce mobility inversion at dilute concentrations and suppress the inversion effect at large concentrations. This re-entrant behavior, previously observed in the aggregation of like-charged polymer solutions, calls for verification by polymer transport experiments.

Bulk nanobubbles in aqueous salt solution

We have investigated the nanobubble generation, characterization, and their stability in monovalent and multivalent salt solution. The solubility of gases in aqueous salt solution decreases with salt concentration and this effect is the so-called “salting out effects” of dissolved gases. The dissolution of salt in water leads to dissociation of salt into ions and presence of water molecules results in solvation of ions. The solvation weakens the affinity of non-polar oxygen molecules in water and thus tends to out the dissolved oxygen from the water molecules. We have experimentally observed that dissolved gas releases in the form of nanobubbles in the bulk liquid. Nanoparticle tracking analysis (NTA) have been used to characterize the size and bubble number density of nanobubbles. The surface charge of the nanobubbles is characterized in terms of zeta potential of the nanobubbles releasing during salting out of the dissolved gases. The effect of the mono and multivalent salts has been investigated. The stability of nanobubbles is reported by measuring the bubble size distribution over the period of time. The nanobubbles are observed to stable for more than 3 days.

Effective Repulsion Between Oppositely Charged Particles in Symmetrical Multivalent Salt Solutions: Effect of Salt Valence

Salt ions play critical roles in the assembly of polyelectrolytes such as nucleic acids and colloids since ions can regulate the effective interactions between them. In this work, we investigated the effective interactions between oppositely charged particles in symmetrical (z:z) salt solutions by Monte Carlo simulations with salt valence z ranging from 1 to 4. We found that the effective interactions between oppositely charged particles are attractive for 1:1 and low multivalent salts, while they become apparently repulsive for high multivalent salts. Moreover, such effective repulsion becomes stronger as z increases from 2 to 3, while it becomes weaker when z increases from 3 to 4. Our analyses reveal that the overall effective interactions are attributed to the interplay between ion translational entropy and electrostatic energy, and the non-monotonic salt-valence dependence of the effective repulsions is caused by the rapid decrease of attractive electrostatic energy between two oppositely charged particles with their over-condensed counterions of opposite charges when z exceeds 3. Our further MC simulations show that the involvement of local-ranged counterion–co-ion repulsions can enhance the effective repulsions through weakening the attractive electrostatic energy, especially for higher salt valence.

Rheological Behavior of a Quaternary Ammonium Copolymer in the Presence of Inorganic Salts

Quaternary ammonium random copolymers poly(methacryloyloxyethyl trimethyl ammonium chloride-co-acrylamide) P(DMC-AM) with either varied cationicities or intrinsic viscosities were synthesized and their structure was analyzed by FTIR and NMR; the results verified the structure of the P(DMC-AM). The rheological behavior of the P(DMC-AM) resulting from its polymer structure (cationicity and intrinsic viscosity) in NaCl aqueous solutions was studied. The results showed that increasing the polymer cationicity could enhance its salt resistance, especially at low cationicity, and the apparent viscosity was in direct proportion to the intrinsic viscosity of the P(DMC-AM) in salt solutions. Furthermore, salt effects (ionic radius, cationic valence, and anion valence) on the apparent viscosity were characterized. They clearly showed that the apparent viscosity was decreased with the increase of ion radius and ion valence. In particular, a difference in polymer aggregation was found when multivalent cations or anions containing solvents were added; two schematic models describing the rheological behavior of the P(DMC-AM) molecules in multivalent salt solutions are proposed.

Viscosity Behavior of P(DAC-AM) with Serial Cationicity and Intrinsic Viscosity in Inorganic Salt Solutions.

The poly(acryloyloxyethyl trimethyl ammonium chloride–co–acrylamide), P(DAC-AM), is a kind of cationic polyelectrolyte usually applied in a solution form, and its performance is affected by its structure and the environment where it is used. In particular, its viscosity properties in salt solutions are directly related to its efficacy in various applications, and the performance is one of the most important solution properties. Therefore, in this paper, the effects of the salt concentration and valence of seven kinds of inorganic salts, NaCl, LiCl, KCl, MgCl2, AlCl3, Na2SO4, and Na3PO4, on the values of apparent viscosity (ηa) of P(DAC-AM) samples with cationicity of 10%, 50%, and 90%, and intrinsic viscosity ([η]) of 5, 10, and 15 dL/g were investigated. The ηa was determined using a rotational viscometer. The interaction mechanism between the polymers and salt ions was also investigated. The results showed that depending on the salt concentration, the ηa firstly decreased sharply to the inflection point which indicated the minimum volume of the molecule shrinking, and then either maintained the value unchanged or increased. The salt concentration corresponding to the inflection point decreased with the increase of the salt ion valence but with the reduction of the cationicity of the polymer. The ηa at the inflection point increased as the [η] of the polymer grew. This indicated that the salt concentration and the salt ion valence had a notable impact on the stretch of the cationic polymer molecule in the salt solutions. It was discovered that the phenomenon of the increase of the ηa of P(DAC-AM) samples in the multivalent salt solutions after the inflection point was caused by not only the increase of the ηa of the complexes formed from the pure salts, but also the viscosity resistance of the charge and volume between the polymer molecules and salt ions, as well as the complexes themselves. The linear relationship between the increased ηa and the salt concentration, representing the interaction both among the complexes themselves and between the polymer and complexes, was obtained. Furthermore, the interaction model between the salt ions and P(DAC-AM) molecules in a wide range of salt concentrations was illustrated.

Predicting Monovalent Ion Correlation Effects in Nucleic Acids.

Ion correlation and fluctuation can play a potentially significant role in metal ion–nucleic acid interactions. Previous studies have focused on the effects for multivalent cations. However, the correlation and fluctuation effects can be important also for monovalent cations around the nucleic acid surface. Here, we report a model, gMCTBI, that can explicitly treat discrete distributions of both monovalent and multivalent cations and can account for the correlation and fluctuation effects for the cations in the solution. The gMCTBI model enables investigation of the global ion binding properties as well as the detailed discrete distributions of the bound ions. Accounting for the ion correlation effect for monovalent ions can lead to more accurate predictions, especially in a mixed monovalent and multivalent salt solution, for the number and location of the bound ions. Furthermore, although the monovalent ion-mediated correlation does not show a significant effect on the number of bound ions, the correlation may enhance the accumulation of monovalent ions near the nucleic acid surface and hence affect the ion distribution. The study further reveals novel ion correlation-induced effects in the competition between the different cations around nucleic acids.

Anomalous Elastic Properties of Attraction-Dominated DNA Self-Assembled 2D Films and the Resultant Dynamic Biodetection Signals of Microbeam Sensors.

The condensation of DNA helices has been regularly found in cell nucleus, bacterial nucleoids, and viral capsids, and during its relevant biodetections the attractive interactions between DNA helices could not be neglected. In this letter, we theoretically characterize the elastic properties of double-stranded DNA (dsDNA) self-assembled 2D films and their multiscale correlations with the dynamic detection signals of DNA-microbeams. The comparison of attraction- and repulsion-dominated DNA films shows that the competition between attractive and repulsive micro-interactions endows dsDNA films in multivalent salt solutions with anomalous elastic properties such as tensile surface stresses and negative moduli; the occurrence of the tensile surface stress for the attraction-dominated DNA self-assembled film reveals the possible physical mechanism of the condensation found in organism. Furthermore, dynamic analyses of a hinged–hinged DNA-microbeam reveal non-monotonous frequency shifts due to attraction- or repulsion-dominated dsDNA adsorptions and dynamic instability occurrence during the detections of repulsion-dominated DNA films. This dynamic instability implies the existence of a sensitive interval of material parameters in which DNA adsorptions will induce a drastic natural frequency shift or a jump of vibration mode even with a tiny variation of the detection conditions. These new insights might provide us some potential guidance to achieve an ultra-highly sensitive biodetection method in the future.

To what extent of ion neutralization can multivalent ion distributions around RNA-like macroions be described by Poisson–Boltzmann theory?**Project supported by the National Natural Science Foundation of China (Grant Nos. 11374234, 11575128, 11774272, and 11647312).

Nucleic acids are negatively charged biomolecules, and metal ions in solutions are important to their folding structures and thermodynamics, especially multivalent ions. However, it has been suggested that the binding of multivalent ions to nucleic acids cannot be quantitatively described by the well-established Poisson–Boltzmann (PB) theory. In this work, we made extensive calculations of ion distributions around various RNA-like macroions in divalent and trivalent salt solutions by PB theory and Monte Carlo (MC) simulations. Our calculations show that PB theory appears to underestimate multivalent ion distributions around RNA-like macroions while can reliably predict monovalent ion distributions. Our extensive comparisons between PB theory and MC simulations indicate that when an RNA-like macroion gets ion neutralization beyond a “critical” value, the multivalent ion distribution around that macroion can be approximately described by PB theory. Furthermore, an empirical formula was obtained to approximately quantify the critical ion neutralization for various RNA-like macroions in multivalent salt solutions, and this empirical formula was shown to work well for various real nucleic acids including RNAs and DNAs.

The effect of microscopic attractive interactions on piezoelectric coefficients of nanoscale DNA films and its resultant mirocantilever-based biosensor signals

The adsorption of charged biomolecules on a substrate will trigger a self-induced electric potential field that could deflect microcantilever biosensors in the nanometer regime. The paper is devoted to a multiscale characterization of the piezoelectric coefficient of double-stranded DNA (dsDNA) films with microscopic attractive interactions in multivalence salt solutions, which has a close relationship with biosensor signals. First, two different analytical models of cantilever deflections based on macroscopic piezoelectric theories or mesoscopic liquid crystal theories were combined in the sense of equivalent deformation in order to bridge the relation between the macroscopic piezoelectric coefficient of an adsorbate film and the sensitivity of its microstructure to surrounding conditions. Second, two interaction potentials of the free energy for repulsion-dominated DNA films in NaCl solution or attraction-repulsion-coexisted DNA films in multivalent salt solutions were used to compare the piezoelectric effect and the resultant cantilever deformation at various packing conditions, such as different packing density, various nucleotide numbers and two packing technologies, i.e. nano-grafting or self-assembling technology. The variational tendency of microcantilever deflections predicted by the present multiscale analytical model agrees well with the related DNA-mirocantilever experiments. Negative piezoelectric coefficient of dsDNA film exists in multivalent salt solutions, and its distinctive size effect with different packing densities and nucleotide numbers provides us with an opportunity to obtain a more sensitive microcantilever sensor by careful control of packing conditions.

Anomalous Protein-Protein Interactions in Multivalent Salt Solution.

The stability of aqueous protein solutions is strongly affected by multivalent ions, which induce ion-ion correlations beyond the scope of classical mean-field theory. Using all-atom molecular dynamics (MD) and coarse grained Monte Carlo (MC) simulations, we investigate the interaction between a pair of protein molecules in 3:1 electrolyte solution. In agreement with available experimental findings of "reentrant protein condensation", we observe an anomalous trend in the protein-protein potential of mean force with increasing electrolyte concentration in the order: (i) double-layer repulsion, (ii) ion-ion correlation attraction, (iii) overcharge repulsion, and in excess of 1:1 salt, (iv) non Coulombic attraction. To efficiently sample configurational space we explore hybrid continuum solvent models, applicable to many-protein systems, where weakly coupled ions are treated implicitly, while strongly coupled ones are treated explicitly. Good agreement is found with the primitive model of electrolytes, as well as with atomic models of protein and solvent.

Molecular dynamics simulations of cylindrical polyelectrolyte brushes in monovalent and multivalent salt solutions

Molecular dynamics simulations are applied to investigate the cylindrical polyelectrolyte brushes in monovalent and multivalent salt solutions. By varying the salt valence and concentration, the brush thickness, shape factor of grafted chains, and distributions of monomers and ions in the solutions are studied. The simulation results show that the single osmotic pressure effect in the brush leads to changes in conformation in the presence of monovalent salt, while the ion exchange effect induces the collapse of the brushes in the multivalent salt solutions. Furthermore, the snapshots combined with the distributions of the end-monomers and the mean bond angles demonstrate a nonuniform stretching picture of the grafted chains, which is different with the chains tethered on the planar surface. The charge ratios between the ions trapped in the brush and the monomers are also calculated to elucidate the details of ion exchange process.

Elastic response of DNA molecules under the action of interfacial traction and stretching: An elastic thin rod model

In a multivalent salt solution, a segment of DNA is modeled as an elastic rod subjected to the interfacial traction. The shooting method is used to calculate the equilibrium configurations of condensed DNA under the action of the longitudinal end-force and interfacial traction simultaneously. The results show that the shapes of DNA are mainly determined by the competition between the interfacial energy and elastic strain energy of stretching. The change of end-to-end distance with the longitudinal end-force is consistent with the worm-like chain (WLC) model. The higher the concentration is, the stronger the condensation of DNA.

Bridging contributions to polyelectrolyte brush collapse in multivalent salt solutions

ABSTRACTPolyelectrolyte brushes are essential in many aspects of surface functionality, particularly for colloidal stabilization and lubrication in biological and materials science applications. It has been shown experimentally that the brushes undergo an abrupt shrinkage in the presence of multivalent counter‐ions. This transition is studied here using a phenomenological mean‐field approach with a model that specifically includes bridging of the polyelectrolyte chains by the multiple charges on the multivalent counter‐ions. Using an energy balance represented by the sum of electrostatic, polymeric and entropic mean‐field terms, additional parameterized phenomenological terms are introduced for counter‐ion condensation and for the attractive interaction between adjacent polyelectrolyte chains to account for the bridging effect. The free energy is minimized with respect to the counter‐ion populations and the brush height. In agreement with experimental observations, increasing the concentration of multivalent ions leads to a sharp collapse of the polyelectrolyte brush height. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016, 54, 284–291

Production of fructose sugar from aqueous solutions: nanofiltration performance and hydrodynamic analysis

Nanofiltration (NF) is a rapidly advancing membrane technique for concentration of sugar and multivalent salt solutions. The performance of indigenously synthesized functionalized polyamide (FPA) nanofiltration membranes of 150 and 250 molecular weight cut off (MWCO) was studied with respect to their ability to concentrate 2% (w/v) aqueous fructose with minimum losses of the sugar in permeate. Water flux and fructose retention properties of the NF membranes were compared to that of commercial reverse osmosis (RO) membranes. At an applied feed pressure of 10 bar, fructose rejection was found to be 94.14, 60.2 and 98.7% for FPA-150, FPA-250 and RO membranes, respectively. Hydrodynamic analysis was performed to study detailed fluid flow profile inside the membrane module to aid design of membrane systems. Economic estimation revealed that nanofiltration by FPA-150 membrane costs just 15.27% of that required by conventional evaporation for treating 1 m3/h fructose, owing to high flux combined with minimum sugar loss.

Polyelectrolyte brushes in monovalent and multivalent salt solutions

Langevin dynamics simulations are performed to study polyelectrolyte brushes by varying the chain grafting density σg, the added salt valence Z, and concentration Cs. The brush thickness H follows a scaling relation in monovalent salt solutions as Cs−0.15, decreasing more slowly than the scaling prediction. In divalent and trivalent salt solutions, H acquires a minimum value at the stoichiometric point, and then levels off and slightly increases, respectively. The shape and orientation of the chains change with Cs accordingly. An electric double layer is formed around the brush rim, revealed by the calculation of vertical charge distribution. Increasing σg, Z, Cs reduces the width of the layer. Side-view density study further shows how the three parameters transform the brush profile from an individual-chain distribution to a homogeneous one. Finally, about 90% of chain charges are neutralized by the ions trapped in the brushes. It is found that ion condensation on the chains can be described by Manning's theory in sparse grafting and dilute salt conditions.

An elastic rod model to evaluate effects of ionic concentration on equilibrium configuration of DNA in salt solution

As a coarse-gained model, a super-thin elastic rod subjected to interfacial interactions is used to investigate the condensation of DNA in a multivalent salt solution. The interfacial traction between the rod and the solution environment is determined in terms of the Young-Laplace equation. Kirchhoff's theory of elastic rod is used to analyze the equilibrium configuration of a DNA chain under the action of the interfacial traction. Two models are established to characterize the change of the interfacial traction and elastic modulus of DNA with the ionic concentration of the salt solution, respectively. The influences of the ionic concentration on the equilibrium configuration of DNA are discussed. The results show that the condensation of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of forces that drive DNA condensation. With the change of concentration, the DNA segments will undergo a series of alteration from the original configuration to the condensed configuration, and the spiral-shape appearing in the condensed configuration of DNA is independent of the original configuration.

On the Continuity of States between DNA-Ordering Transitions in Mono- and Multi-Valent Salt Solutions

At the increasing density imposed by external osmotic pressure, DNA in monovalent salt solutions (e.g., NaCl) to goes through a set of ordered mesophases, finally crystallizing into an orthorhombic crystal. While the transition from the (chiral) nematic to the line-hexatic phase has been observed before, it is still unclear whether the transition is of second order or weak first order. In multivalent salt solutions (e.g., CoHex = Co(NH3)6 Cl3), DNA is known to collapse into an ordered aggregate under osmotic pressure, or even at zero osmotic pressure at large enough concentrations of the multivalent salt. It has remained unclear what is the connection between these two ordering transitions -- with vs. without CoHex. By using a novel method of temperature-regulating the osmotic stress imposed on the DNA subphase, we show that there exists a continuity of states between these two ordering transitions and that they are of the same type. We use the small but accurately measurable temperature dependence of the osmotic pressure of a PEG solution to fine-regulate the osmotic stress with which it acts on the DNA subphase. This allows us to set the osmotic pressure to an accuracy never achieved before. This advance in experimental methodology allows us then to detect small but nevertheless finite changes in the density of DNA as it goes through the ordering transitions. In this way, we first determine experimentally the small density change that occurs at the (chiral) nematic to line-hexatic phase transition. For Na-DNA, this density change can be translated into a ∼1.5 Angstrom change in the interaxial spacing. This density discontinuity at the phase transition either does not depend on the NaCl concentration or varies by < 0.1 Angstrom as the salt concentration is varied.