Monte Carlo simulation of electrical double-layer formation from mixtures of electrolytes inside nanopores

The formation of the electrical double layer (EDL) in the presence of trivalent and monovalent ions inside a slit-type nanopore was simulated via the canonical Monte Carlo method using a primitive model. In large pores, the distribution of ionic species is similar to that observed in an isolated planar double layer. Screening of surface charge is determined by the competitive effects between ion size and charge asymmetry of the counterions. On the other hand, as the pore size approaches the dimension of the ionic species, phenomena such as EDL overlapping become enhanced by ion-size effects. Simulation results demonstrate that EDL overlapping is not only a function of such parameters as ionic strength and surface charge density, but also a function of the properties of the ionic species involved in the EDL. Furthermore, charge inversion can be observed under certain conditions when dealing with mixtures of asymmetric electrolytes. This phenomenon results from strong ion-ion correlation effects and the asymmetries in size and charge of ionic species, and is most significant in the case of trivalent counterions with larger diameters. The simulation results provide insights into the fundamental mechanisms behind the formation of EDL within nanopores as determined by pore size and by the properties of ionic species present in solution. The findings of this work are relevant to ion sorption and transport within nanostructured materials.     

A size-modified poisson–boltzmann ion channel model in a solvent of multiple ionic species: Application to voltage-dependent anion channel

We present a new size-modified Poisson–Boltzmann ion channel (SMPBIC) model and use it to calculate the electrostatic potential, ionic concentrations, and electrostatic solvation free energy for a voltage-dependent anion channel (VDAC) on a biological membrane in a solution mixture of multiple ionic species. In particular, the new SMPBIC model adopts a membrane surface charge density and a natural Neumann boundary condition to reflect the charge effect of the membrane on the electrostatics of VDAC. To avoid the singularity difficulties caused by the atomic charges of VDAC, the new SMPBIC model is split into three submodels such that the solution of one of the submodels is obtained analytically and contains all the singularity points of the SMPBIC model. The other two submodels are then solved numerically much more efficiently than the original SMPBIC model. As an application of this SMPBIC submodel partitioning scheme, we derive a new formula for computing the electrostatic solvation free energy. Numerical results for a human VDAC isoform 1 (hVDAC1) in three different salt solutions, each with up to five different ionic species, confirm the significant effects of membrane surface charges on both the electrostatics and ionic concentrations. The results also show that the new SMPBIC model can describe well the anion selectivity property of hVDAC1, and that the new electrostatic solvation free energy formula can significantly improve the accuracy of the currently used formula. © 2019 Wiley Periodicals, Inc.     

Internal and free energy in a pair of like-charged colloids: Monte Carlo simulations

The effective interaction between two colloidal particles in a bath of monovalent co- and counterions is studied by means of lattice Monte Carlo simulations with the primitive model. The internal electrostatic energy as a function of the colloid distance is studied fixing the position of the colloids. The free energy of the whole system is obtained introducing a bias parabolic potential, that allows us to sample efficiently small separations between the colloidal particles. For small charges, both the internal and free energy increase when the colloids approach each other, resulting in an effective repulsion driven by the electrostatic repulsion. When the colloidal charge is large enough, on the other hand, the colloid-ion coupling is strong enough to form double layers. The internal energy in this case decreases upon approaching the colloids because more ions enter the double layer. This attractive contribution to the interaction between the colloids is stronger for larger charges and larger ionic concentrations. However, the total free energy increases due to the loss of ionic entropy, and resulting finally in a repulsive interaction potential driven by the entropic contributions. The loss of ionic entropy can be almost quantitatively reproduced with the ideal contribution, the same level of approximation as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The overall behavior is captured by the DLVO theory qualitatively, and a comparison is made with the functional form predicted by the theory, showing moderate agreement.     

利用基于Gouy-Chapman模型的离子有效电荷定量表征离子特异性效应

离子特异性效应在固-液界面反应中是普遍存在的.近期研究指出,在较低电解质浓度的某些体系中,离子特异性效应可能并非来源于色散力、经典诱导力、离子半径或水合半径的大小等,而是界面附近强电场中的离子极化作用.这种作用可使界面附近的吸附态反号离子被强烈极化(高达经典极化的104倍).强烈极化的结果将导致离子在界面附近受到的库仑力远远超过离子电荷所能产生的库仑力,这体现在离子的有效电荷将远大于离子的实际电荷.因此胶体体系中基于这种强极化的离子有效电荷可以用来定量表征离子特异性效应的强度.本研究在蒙脱石-胡敏酸混合悬液凝聚过程中发现了Na+、K+、Ca2+、Cu2+四种离子的离子特异性效应,提出了基于激光散射技术测定离子有效电荷的方法,并成功获得了被强烈极化后的离子有效电荷数值.实验测得的Na+、K+、Ca2+、Cu2+四种离子的有效电荷值分别为:ZNa(effective)=1.46,ZK(effective)=1.86,ZCa(effective)=3.92,ZCu(effective)=6.48.该结果表明:(1)离子在强电场中的极化将大大提高离子的有效电荷,从而极大地增强离子所受的库仑作用力;(2)离子的电子层数越多,离子极化越强烈,离子的有效电荷增加越多.     

Charge asymmetries in hydration of polar solutes

We study the solvation of polar molecules in water. The center of water's dipole moment is offset from its steric center. In common water models, the Lennard-Jones center is closer to the negatively charged oxygen than to the positively charged hydrogens. This asymmetry of water's charge sites leads to different hydration free energies of positive versus negative ions of the same size. Here, we explore these hydration effects for some hypothetical neutral solutes, and two real solutes, with molecular dynamics simulations using several different water models. We find that, like ions, polar solutes are solvated differently in water depending on the sign of the partial charges. Solutes having a large negative charge balancing diffuse positive charges are preferentially solvated relative to those having a large positive charge balancing diffuse negative charges. Asymmetries in hydration free energies can be as large as 10 kcal/mol for neutral benzene-sized solutes. These asymmetries are mainly enthalpic, arising primarily from the first solvation shell water structure. Such effects are not readily captured by implicit solvent models, which respond symmetrically with respect to charge.     

Influence of monovalent ion size on colloidal forces probed by Monte Carlo simulations

The present work studies the role of ionic size in the interactions between the electrical double layers of colloids immersed into electrolyte solutions of monovalent ions. Such interactions are studied by means of Monte Carlo (MC) simulations and the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Despite the omission of the steric effects and some other features of real electrolyte solutions, DLVO theory is known to work qualitatively well for 1:1 electrolyte solutions. However, this affirmation is based on previous tests where an ionic diameter around 0.4 nm was taken for all ionic species. In contrast, some experimental studies suggest that larger hydrated ions should be considered and even specified for each type of ion. In this work, the importance of ionic size is analyzed by applying the primitive model of electrolyte to the intermediate region between a pair of equally charged infinite planar surfaces. The double layer interactions were calculated from the ionic densities at the distance of closest approach to the charged surfaces, this method constitutes an alternative to the traditional calculations at the midplane. Our MC simulations predict the existence of negative net pressures for monovalent electrolytes in the case of zero charge density. In addition, MC simulations reveal some disagreements with theoretical predictions for ionic diameters larger than 0.4 nm. These discrepancies can become significant if surface charge density is large enough due to the restructuration of the double layer. The physical mechanisms for these deviations are also discussed.     

Ionic electrets: electrostatic charging of surfaces by transferring mobile ions upon contact

This paper describes the fabrication and characterization of ionic electrets-materials that bear a long-lived electrostatic charge because of an imbalance between the number of cationic and anionic charges in the material. Crosslinked polystyrene microspheres that contain covalently bound ions and mobile counterions transfer some of their mobile ions in air, in the absence of bulk liquid, to another material upon contact. According to the ion-transfer model of contact electrification, this selective transfer of mobile ions yields microspheres that have a net electrostatic charge. A tool that operates on the principle of electrostatic induction measures the charge on individual microspheres (50-450 microm in diameter). Microspheres with a variety of covalently bound ionic functional groups (tetraalkylammonium, alkyltriphenylphosphonium, alkylsulfonate, and arylsulfonate) acquire charges consistent with this ion-transfer mechanism. The charge on a microsphere is proportional to its surface area (ca. 1 elementary charge per 2000 nm2) and close to the theoretical limit imposed by the dielectric breakdown of air. The charge density in an atmosphere of SF6 is more than twice that in an atmosphere of N2. These observations suggest that the charge density of these ionic electret microspheres is limited by the dielectric breakdown of the surrounding gas. Functionalizing the surfaces of glass or silicon with covalently bound ions and mobile counterions generates ionic electrets from these inorganic substrates. Soft lithography can pattern charge on a planar silicon surface (with oxide) and on the surface of 250-mum glass microspheres.     

Electrode screening by ionic liquids

In this work we are concerned with the short-range screening provided by the ionic liquid dimethylimidazolium chloride near a charged wall. We study the free energy profiles (or potentials of mean force) for charged and neutral solutes as a function of distance from a charged wall. Four different wall charge densities are used in addition to a wall with zero charge. The highest magnitude of the charge densities is ±1 e nm(-2) which is close to the maximum limit of charge densities accessible in experiments, while the intermediate charges ±0.5 e nm(-2) are in the range of densities typically used in most of the experimental studies. Positively and negatively charged solutes of approximately the size of a BF ion and a Cl(-) ion are used as probes. We find that the ionic liquid provides excellent electrostatic screening at a distance of 1-2 nm. The free energy profiles show minima which are due to layering in the ionic liquid near the electrodes. This indicates that the solute ions tend to displace ionic liquid ions in the layers when approaching the electrode. The important role of non-electrostatic forces is demonstrated by the oscillations in the free energy profiles of uncharged solutes as a function of distance from the wall.     

利用基于Gouy-Chapman模型的离子有效电荷定量表征离子特异性效应

离子特异性效应在固-液界面反应中是普遍存在的. 近期研究指出, 在较低电解质浓度的某些体系中, 离子特异性效应可能并非来源于色散力、经典诱导力、离子半径或水合半径的大小等, 而是界面附近强电场中的离子极化作用. 这种作用可使界面附近的吸附态反号离子被强烈极化(高达经典极化的10⁴倍). 强烈极化的结果将导致离子在界面附近受到的库仑力远远超过离子电荷所能产生的库仑力, 这体现在离子的有效电荷将远大于离子的实际电荷. 因此胶体体系中基于这种强极化的离子有效电荷可以用来定量表征离子特异性效应的强度. 本研究在蒙脱石-胡敏酸混合悬液凝聚过程中发现了Na⁺、K⁺、Ca²⁺、Cu²⁺四种离子的离子特异性效应, 提出了基于激光散射技术测定离子有效电荷的方法, 并成功获得了被强烈极化后的离子有效电荷数值. 实验测得的Na⁺、K⁺、Ca²⁺、Cu²⁺四种离子的有效电荷值分别为: Z_{Na(effective)}=1.46, Z_K(effective)=1.86, Z_{Ca(effective)}=3.92, Z_{Cu(effective)}=6.48.该结果表明: (1) 离子在强电场中的极化将大大提高离子的有效电荷, 从而极大地增强离子所受的库仑作用力;(2) 离子的电子层数越多, 离子极化越强烈, 离子的有效电荷增加越多.     

Hydrophobic and ionic interactions in nanosized water droplets

A number of situations such as protein folding in confined spaces, lubrication in tight spaces, and chemical reactions in confined spaces require an understanding of water-mediated interactions. As an illustration of the profound effects of confinement on hydrophobic and ionic interactions, we investigate the solvation of methane and methane decorated with charges in spherically confined water droplets. Free energy profiles for a single methane molecule in droplets, ranging in diameter (D) from 1 to 4 nm, show that the droplet surfaces are strongly favorable as compared to the interior. From the temperature dependence of the free energy in D = 3 nm, we show that this effect is entropically driven. The potentials of mean force (PMFs) between two methane molecules show that the solvent separated minimum in the bulk is completely absent in confined water, independent of the droplet size since the solute particles are primarily associated with the droplet surface. The tendency of methanes with charges (M(q+) and M(q-) with q(+) = |q(-)| = 0.4e, where e is the electronic charge) to be pinned at the surface depends dramatically on the size of the water droplet. When D = 4 nm, the ions prefer the interior whereas for D < 4 nm the ions are localized at the surface, but with much less tendency than for methanes. Increasing the ion charge to e makes the surface strongly unfavorable. Reflecting the charge asymmetry of the water molecule, negative ions have a stronger preference for the surface compared to positive ions of the same charge magnitude. With increasing droplet size, the PMFs between M(q+) and M(q-) show decreasing influence of the boundary owing to the reduced tendency for surface solvation. We also show that as the solute charge density decreases the surface becomes less unfavorable. The implications of our results for the folding of proteins in confined spaces are outlined.     

Hofmeister effects: interplay of hydration, nonelectrostatic potentials, and ion size

The classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloids, and corresponding theories of electrolytes, are unable to explain ion specific forces between colloidal particles quantitatively. The same is true generally, for surfactant aggregates, lipids, proteins, for zeta and membrane potentials and in adsorption phenomena. Even with fitting parameters the theory is not predictive. The classical theories of interactions begin with continuum solvent electrostatic (double layer) forces. Extensions to include surface hydration are taken care of with concepts like inner and outer Helmholtz planes, and "dressed" ion sizes. The opposing quantum mechanical attractive forces (variously termed van der Waals, Hamaker, Lifshitz, dispersion, nonelectrostatic forces) are treated separately from electrostatic forces. The ansatz that separates electrostatic and quantum forces can be shown to be thermodynamically inconsistent. Hofmeister or specific ion effects usually show up above ≈10(-2) molar salt. Parameters to accommodate these in terms of hydration and ion size had to be invoked, specific to each case. Ionic dispersion forces, between ions and solvent, for ion-ion and ion-surface interactions are not explicit in classical theories that use "effective" potentials. It can be shown that the missing ionic quantum fluctuation forces have a large role to play in specific ion effects, and in hydration. In a consistent predictive theory they have to be included at the same level as the nonlinear electrostatic forces that form the skeletal framework of standard theory. This poses a challenge. The challenges go further than academic theory and have implications for the interpretation and meaning of concepts like pH, buffers and membrane potentials, and for their experimental interpretation. In this article we overview recent quantitative developments in our evolving understanding of the theoretical origins of specific ion, or Hofmeister effects. These are demonstrated through an analysis that incorporates nonelectrostatic ion-surface and ion-ion dispersion interactions. This is based on ab initio ionic polarisabilities, and finite ion sizes quantified through recent ab initio work. We underline the central role of ionic polarisabilities and of ion size in the nonelectrostatic interactions that involve ions, solvent molecules and interfaces. Examples of mechanisms through which they operate are discussed in detail. An ab initio hydration model that accounts for polarisabilities of the tightly held hydration shell of "cosmotropic" ions is introduced. It is shown how Hofmeister effects depend on an interplay between specific surface chemistry, surface charge density, pH, buffer, and counterion with polarisabilities and ion size. We also discuss how the most recent theories on surface hydration combined with hydrated nonelectrostatic potentials may predict experimental zeta potentials and hydration forces.     

Incidence of partial charges on ion selectivity in potassium channels

Potassium channels are membrane proteins known to select potassium over sodium ions at a high diffusion rate. We conducted ab initio calculations on a filter model of KcsA of about 300 atoms at the Hartree-Fock level of theory. Partial charges were derived from the quantum mechanically determined electrostatic potential either with Merz-Kollman or Hinsen-Roux schemes. Large polarization and/or charge transfer occur on potassium ions located in the filter, while the charges on sodium ions remain closer to unity. As a result, a weaker binding is obtained for K(+) ions. Using a simplified version of a permeation model based on the concerted-motion mechanism for ion translocation within the single-file ion channel [P. H. Nelson, J. Chem. Phys. 117, 11396 (2002)], we discuss how differences in polarization effects in the adducts with K(+) and Na(+) can play a role as for ionic selectivity and conductance.     

Microscopic and semimicroscopic calculations of electrostatic energies in proteins by the POLARIS and ENZYMIX programs

Different microscopic and semimicroscopic approaches for calculations of electrostatic energies in macromolecules are examined. This includes the Protein Dipoles Langevin Dipoles (PDLD) method, the semimicroscopic PDLD (PDLD/S) method, and a free energy perturbation (FEP) method. The incorporation of these approaches in the POLARIS and ENZYMIX modules of the MOLARIS package is described in detail. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions, as well as the effects of the ionic strength and external pH. Determination of the hydrophobic energy involves an approach that considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. Ionic strength effects are studied by modeling the ionic environment around the given system using a grid of residual charges and evaluating the relevant interaction using Coulomb's law with the dielectric constant of water. The performance of the FEP calculations is significantly enhanced by using special boundary conditions and evaluating the long-range electrostatic contributions using the Local Reaction Field (LRF) model. A diverse set of electrostatic effects are examined, including the solvation energies of charges in proteins and solutions, energetics of ion pairs in proteins and solutions, interaction between surface charges in proteins, and effect of ionic strength on such interactions, as well as electrostatic contributions to binding and catalysis in solvated proteins. Encouraging results are obtained by the microscopic and semimicroscopic approaches and the problems associated with some macroscopic models are illustrated. The PDLD and PDLD/S methods appear to be much faster than the FEP approach and still give reasonable results. In particular, the speed and simplicity of the PDLD/S method make it an effective strategy for calculations of electrostatic free energies in interactive docking studies. Nevertheless, comparing the results of the three approaches can provide a useful estimate of the accuracy of the calculated energies. © 1993 John Wiley & Sons, Inc.     

A new surface structural approach to ion adsorption: tracing the location of electrolyte ions

Electrolyte ions differ in size leading to the possibility that the distance of closest approach to a charged surface differs for different ions. So far, ions bound as outersphere complexes have been treated as point charges present at one or two electrostatic plane(s). However, in a multicomponent system, each electrolyte ion may have its own distance of approach and corresponding electrostatic plane with an ion-specific capacitance. It is preferable to make the capacitance of the compact part of the double layer a general characteristic of the solid-solution interface. A new surface structural approach is presented that may account for variation in size of electrolyte ions. In this approach, the location of the charge of the outersphere surface complexes is described using the concept of charge distribution in which the ion charge is allowed to be distributed over two electrostatic planes. It was shown that the concept can successfully describe the pH dependent proton binding and the shift in the isoelectric point (IEP) in the presence of variety of monovalent electrolyte ions, including Li(+), Na(+), K(+), Cs(+), Cl(-), NO(-)(3), and ClO(-)(4) with a common set of parameters. The new concept also sheds more light on the degree of hydration of the ions when present as outersphere complexes. Interpretation of the charge distribution values obtained shows that Cl(-) ions are located relatively close to the surface. The large alkali ions K(+), Cs(+), and Rb(+) are at the largest distance. Li(+), Na(+), NO(-)(3), and ClO(-)(4) are present at intermediate positions.     

On the survival of peptide cations after electron capture: Role of internal hydrogen bonding and microsolvation

Electron capture by both bare and microsolvated small peptide dications was investigated by colliding these ions with sodium vapor in an accelerator mass spectrometer to provide insight into processes that occur on the microsecond time frame. Survival of the intact peptide monocation after electron capture depends strongly on molecular size. For dipeptides, no intact reduced species were observed; the predominant ions correspond to loss of hydrogen and ammonia. In contrast, the intact reduced species was observed for larger peptides. Calculated structures indicate that the diprotonated dipeptide ions form largely extended structures with low probability of internal ionic hydrogen bonding (i.e., charge solvation) whereas internal ionic H-bonding occurs extensively for larger peptide dications. Solvation of the peptide ions with between one to seven methanol molecules reduces the total extent of H loss even for dipeptides where intact reduced species can survive more than a microsecond after electron capture. The yield of ions corresponding to cleavage of NCalpha bonds (c+ and z+* ions) does not depend strongly on peptide size but decreases with the extent of microsolvation for the dipeptide dications. H-bonding appears to play an important role for the survival of the intact reduced ions but less so for the formation of c+ and z+* ions. Our results indicate that electron capture predominantly occurs at the ammonium groups (at least 70 to 80%), and provides important new insights into the electron capture dissociation process.     

Theoretical investigations of the dissociation of charged protein complexes in the gas phase

A series of calculations, varying from simple electrostatic to more detailed semi-empirical based molecular dynamics ones, were carried out on charged gas phase ions of the cytochrome c(') dimer. The energetics of differing charge states, charge partitionings, and charge configurations were examined in both the low and high charge regimes. As well, preliminary free energy calculations of dissociation barriers are presented. It is shown that one must always consider distributions of charge configurations, once protein relaxation effects are taken into account, and that no single configuration dominates. All these results also indicate that in the high charge limit, the dissociation of protein complex ions is governed by electrostatic repulsion from the net charges, the consequences of which are enumerated and discussed. There are two main trends deriving from this, namely that charges will move so as to approximately maintain constant surface charge density, and that the lowest barrier to dissociation is the one that produces fragment ions with equal charges. In particular, it is shown that the charge-to-mass ratio of a fragment ion is not the key physical parameter in predicting dissociation products. In fact, from the perspective of the division of total charge, many dissociation pathways reported to be "asymmetric" in the literature should be more properly labelled as "symmetric" or "near-symmetric". The Coulomb repulsion model assumes that the timescale for charge transfer is faster than that for protein structural changes, which in turn is faster than that for complex dissociation.     

Computer simulation of ion cluster speciation in concentrated aqueous solutions at ambient conditions

Dynamic simulations are used to investigate ion cluster formation in unsaturated aqueous NaCl at 25 degrees C. Statistical, structural, and dynamic properties are reported. An effort is made to identify general behaviors that are expected to hold beyond the limitations of the force field. Above approximately 1 M, clusters with more than ten ions begin to form after approximately 10-20 ns of simulation time, but no evidence of irreversible ion aggregation is observed. Cluster survival times are estimated, showing that the kinetics become increasingly complex as salt is added, leading to multiple decay rates. Cluster dipole moment distributions show characteristic peaks that reflect the preferred conformations of clusters in solution. These are modulated by electrostatic and liquid-structure forces and are described in detail for clusters of up to five ions. For a given size and charge, the cluster morphology is independent of salt concentration. Below approximately 2 M, clusters affect the structure of water in their first hydration shells, so dipole moments parallel to the cluster macrodipoles are induced. These effects show a weak dependence with concentration below approximately 2 M, but vanish in the 2-3 M range. A possible connection with the structural transition recently suggested by NMR data in concentrated electrolytes is discussed. The effects of electrostatics on cluster speciation and morphology are discussed based on results from a set of simulations carried out with the ionic charges removed.     

Approaches to hydration, old and new: Insights through Hofmeister effects

Hydration effects in colloidal interactions or problems involving electrolytes are usually taken care of by effective electrostatic potentials that subsume notions like hydrated ion size, Gurney potentials, soft and hard, chaotropic and cosmotropic ions, and inner and outer Helmholtz planes. Quantum fluctuation (dispersion) forces between ions and between ions and surfaces are missing from classical theories, at least not explicit in standard approaches to hydration. This paper outlines an evolving back-to-basics approach that allows these ion specific forces to be included in theories quantitatively. In this approach ab initio quantum mechanics is used to calculate dynamic polarisabilities of ions and to quantify bare ion radii. The ionic dispersion potentials between ions, and between ions and surfaces in water can then be given explicit analytic form from an extension of Lifshitz theory. They are included in the theory along with electrostatic potentials. In a first stage the primitive (continuum solvent) model provides a skeletal theory on which to build in hydration. Extension of the ab initio calculations to include “dressed” ions, i.e. water hydration shells for cosmotropic ions, quadrupolar and octupolar polarisability contributions and; for colloids, allowance for a surface hydration layer, permits quantification of Hofmeister effects and Gurney potentials. With these extensions, primary hydration forces (short range repulsion) arise due to an interplay between surface hydration layers and specific ion interactions. Apparent longer range “secondary hydration forces” are shown to be a consequence of ion-surface dispersion interactions and are not true “hydration forces”.