Ion permeation dynamics in carbon nanotubes

Molecular dynamics simulations are carried out to investigate the permeation of ions and water in a membrane consisting of single wall carbon nanotubes possessing no surface charges connecting two reservoirs. Our simulations reveal that there are changes in the first hydration shell of the ions upon confinement in tubes of 0.82 or 0.90 nm effective internal diameter. Although the first minimum in the g(r) is barely changed in the nanotube compared to in the bulk solution, the hydration number of Na(+) ion is reduced by 1.0 (from 4.5 in bulk to 3.5 in the 0.90 nm tube) and the hydration number is reduced further in the 0.82 nm tube. The changes in the hydration shell of Cl(-) ion are negligible, within statistical errors. The water molecules of the first hydration shell of both ions exchange less frequently inside the tube than in the bulk solution. We compare ion trajectories for ions in the same tube under identical reservoir conditions but with different numbers of ions in the tubes. This permits investigation of changes in structure and dynamics which arise from multiple ion occupancy in a carbon nanotube possessing no surface charges. We also investigated the effects of tube flexibility. Ions enter the tubes so as to form a train of ion pairs. We find that the radial distribution profiles of Na(+) ions broaden significantly systematically with increasing number of ion pairs in the tube. The radial distribution profiles of Cl(-) ions change only slightly with increasing number of ions in the tube. Trajectories reveal that Na(+) ions do not pass each other in 0.90 nm tubes, while Cl(-) ions pass each other, as do ions of opposite charge. An ion entering the tube causes the like-charged ions preceding it in the tube to be displaced along the tube axis and positive or negative ions will exit the tube only when one or two other ions of the same charge are present in the tube. Thus, the permeation mechanism involves multiple ions and Coulomb repulsion among the ions plays an essential role.     

Structure of electrolyte solutions sorbed in carbon nanospaces, studied by the replica RISM theory

The replica RISM theory is used to investigate the structure of electrolyte solutions confined in carbonized polyvinylidene chloride (PVDC) nanoporous material, compared to bulk electrolyte solution. Comparisons are made between the models of electrolyte solution sorbed in the carbonized PVDC material and a single carbon nanosphere in bulk electrolyte solution. Particular attention is paid to the chemical potential balance between the species of the sorbed electrolyte solution and the bulk solution in contact with the nanoporous material. As a result of the strong hydrophobicity of the carbonized PVDC material in the absence of activating chemical groups, the densities of water and ions sorbed in the material are remarkably low compared to those in the ambient bulk solution. The interaction between water molecules and cations becomes strong in nanospaces. It turns out that, in carbon nanopores, a cation adsorbed at the carbon surface is fully surrounded by the hydration shell of water molecules which separates the cation and the surface. Distinctively, an anion is adsorbed in direct contact with the carbon surface, which squeezes a part of its hydration shell out. The tendency increases toward smaller cations, which are characterized as "positive hydration" ions. In the bulk, cations are not hydrated so strongly and behave similarly to anions. The results suggest that the specific capacitance of an electric double-layer supercapacitor with nanoporous electrodes is intimately related to the solvation structure of electrolyte solution sorbed in nanopores, which is affected by the microscopic structure of the nanoporous electrode.     

Hydration of alkali ions from first principles molecular dynamics revisited

Structural and dynamical properties of the hydration of Li(+), Na(+), and K(+) in liquid water at ambient conditions were studied by first principles molecular dynamics. Our simulations successfully captured the different hydration behavior shown by the three alkali ions as observed in experiments. The present analyses of the dependence of the self-diffusion coefficient and rotational correlation time of water on the ion concentration suggest that Li(+) (K(+)) is certainly categorized as a structure maker (breaker), whereas Na(+) acts as a weak structure breaker. An analysis of the relevant electronic structures, based on maximally localized Wannier functions, revealed that the dipole moment of H(2)O molecules in the first solvation shell of Na(+) and K(+) decreases by about 0.1 D compared to that in the bulk, due to a contraction of the oxygen lone pair orbital pointing toward the metal ion.     

Simulation of Ca2+ and Mg2+ solvation using polarizable atomic multipole potential

The alkaline earth metals calcium and magnesium are critically involved in many biomolecular processes. To understand the hydration thermodynamics of these ions, we have performed molecular dynamics simulations using a polarizable potential. Particle-mesh Ewald for point multipoles has been applied to the calculation of electrostatic interactions. The parameters in this model have been determined from an ab initio quantum mechanical calculation of dimer interactions between ions and water. Two methods for ion solvation free energy calculation, free energy perturbation, and the Bennett acceptance ratio have been compared. Both predict results consistent with other theoretical estimations while the Bennett approach leads to a much smaller statistical error. Based on the Born theory and the ion-oxygen radial distribution functions, we estimate the effective size of the ions in solution, concluding that K(+) > Na(+) congruent with Ca(2+) > Mg(2+). There appears to be much stronger perturbation in water structure, dynamics, and dipole moment around the divalent cations than the monovalent K(+) and Na(+). The average water coordination numbers for Ca(2+) and Mg(2+) are 7.3 and 6, respectively. The lifetime of water molecules in the first solvation shell of Mg(2+) is on the order of hundreds of picoseconds, in contrast to only few picoseconds for Ca(2+), K(+), or Na(+).     

Solvation of calcium ions in methanol-water mixtures: molecular dynamics simulation

Molecular dynamics simulations of CaCl2 solutions in water and methanol-water mixtures, with methanol concentrations of 5, 10, 50, and 90 mol %, at room temperature, have been performed. The methanol and water molecules have been modeled as flexible three-site bodies. Solvation of the calcium ions has been discussed on the basis of the radial and angular distribution functions, the orientation of the solvent molecules, and their geometrical arrangement in the coordination shells. Analysis of the H-bonds of the solvent molecules coordinated by Ca2+ has been done. Residence time of the solvent molecules in the coordination shell has been calculated. The preferential hydration of the calcium ions has been found over the whole range of the mixture composition. The water concentration in the first and second coordination shells of Ca2+ significantly exceeds the water content in the solution, despite the very similar interaction energy of the calcium ion with water and methanol. In aqueous solution and methanol-water mixtures, the first coordination shell of Ca2+ is irregular and long-living. The solvent molecules prefer the anti-dipole arrangement, but, in aqueous solutions and water-rich mixtures, the water molecules in the primary shell have only one H-bonded neighbor.     

Solvation of cations in the LiNO3-Ca(NO3)2-H2O system at 25°C. A molecular dynamics simulation study

A series of solutions of the ternary LiNO₃-Ca(NO₃)₂-H₂O system is simulated under standard conditions by means of classical molecular dynamics (MD). Several variants of the potentials of interparticle interactions predicting different structures and compositions of the lithium cation hydration shell are used in the calculations. The coordination numbers of ions, the mean residence times of water molecules and nitrate anions in the solvation shells of cations, and the self-diffusion coefficients of solution components are estimated for all of the investigated systems. The structural features of the solvation shells of cations in multicomponent aqueous solutions are described on the basis of the obtained data.     

Hydration force between mica surfaces in aqueous KCl electrolyte solution

Liquid-vapor molecular dynamics simulations are performed to study the interaction forces between two mica surfaces in an aqueous KCl electrolyte solution. Strong repulsive hydration force is obtained within a distance of ~2 nm between the two mica surfaces, which cannot be explained by the continuum theory of double-layer repulsion. We find that this short-range repulsive hydration force is much stronger than the double-layer force between mica surfaces. Whereas the simulation system is much smaller than the surface force measurement system, fundamental mechanisms of repulsive hydration force are revealed. In particular, important features of the step-like force oscillatory behavior during normal compression and force hysteresis during retraction are observed. Detailed analysis of the ionic density distributions shows that the "forced adsorption" of diffusive K(+) ions onto mica surfaces during compression and the subsequent "slow desorption" of the absorbed K(+) ions from mica surfaces upon retraction are responsible for the hysteresis phenomenon. From a mechanics point of view, we attribute the load bearing capacity of the dense electrolyte to the very hard hydration shells of K(+) metal ions under confinement. We find that the hydrated K(+) ions and Cl(-) co-ions remain very diffusive in the aqueous film. Water molecules in the hydration layer are also very fluidic, in the sense that the diffusion constant of water molecules is less than its bulk value by at most 3 orders of magnitude under the extreme confinement.     

纳米受限下溶质水化结构的分子模拟

利用分子动力学模拟研究了五种不同种类的溶质分子(K+, Mg2+, Cl-, K-和K0)在直径为0.60-1.28 nm的纳米碳管内的水化结构. 模拟结果揭示了单电荷溶质、双电荷溶质和中性溶质在受限条件下具有不同的水化行为. 单价溶质的配位数只有在直径不大于0.73 nm的纳米碳管内才会明显减少. 和带有电荷的溶质不同, 中性溶质的配位数对纳米碳管直径的改变非常敏感, 并且随着管径的减小而迅速减少. 模拟结果还表明带单价正电荷的溶质(K+)第一配位层水分子的取向结构会随着纳米碳管直径的改变发生变化, 而其他溶质配位层取向结构在本文所涉及的纳米碳管内都几乎和体相中一致. 在直径大于1.0 nm的纳米碳管中, K+的配位层取向结构有序度随着管径的减小而单调下降, 但是在直径小于1.0 nm的纳米碳管中, 随着碳管管径的减小而迅速上升. 在两个最窄的纳米碳管内, 其结构有度甚至高于体相. 双电荷溶质的水化结构在本文所研究的碳管直径范围内和体相完全一致, 即使在直径只有0.6 nm的碳管内也无任何改变.     

Coordination polyhedra of hydration shells of Na+ and K+ cations in aqueous solutions

Simulation of the hydration of Na⁺ and K⁺ cations in dilute solution was performed by the Monte Carlo method. A novel approach to structural analysis of hydration shells of ions was developed. Specific sets of coordination polyhedra formed by water molecules of the first coordination sphere were found. Structural and energy characteristics of hydration were calculated. The effect of Na⁺ and K⁺ cations on the structure of the network of H-bonds and mobility of water molecules in hydration shells was studied. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 852–857, May, 1999.     

A study of the hydration of the alkali metal ions in aqueous solution

The hydration of the alkali metal ions in aqueous solution has been studied by large angle X-ray scattering (LAXS) and double difference infrared spectroscopy (DDIR). The structures of the dimethyl sulfoxide solvated alkali metal ions in solution have been determined to support the studies in aqueous solution. The results of the LAXS and DDIR measurements show that the sodium, potassium, rubidium and cesium ions all are weakly hydrated with only a single shell of water molecules. The smaller lithium ion is more strongly hydrated, most probably with a second hydration shell present. The influence of the rubidium and cesium ions on the water structure was found to be very weak, and it was not possible to quantify this effect in a reliable way due to insufficient separation of the O-D stretching bands of partially deuterated water bound to these metal ions and the O-D stretching bands of the bulk water. Aqueous solutions of sodium, potassium and cesium iodide and cesium and lithium hydroxide have been studied by LAXS and M-O bond distances have been determined fairly accurately except for lithium. However, the number of water molecules binding to the alkali metal ions is very difficult to determine from the LAXS measurements as the number of distances and the temperature factor are strongly correlated. A thorough analysis of M-O bond distances in solid alkali metal compounds with ligands binding through oxygen has been made from available structure databases. There is relatively strong correlation between M-O bond distances and coordination numbers also for the alkali metal ions even though the M-O interactions are weak and the number of complexes of potassium, rubidium and cesium with well-defined coordination geometry is very small. The mean M-O bond distance in the hydrated sodium, potassium, rubidium and cesium ions in aqueous solution have been determined to be 2.43(2), 2.81(1), 2.98(1) and 3.07(1) ?, which corresponds to six-, seven-, eight- and eight-coordination. These coordination numbers are supported by the linear relationship of the hydration enthalpies and the M-O bond distances. This correlation indicates that the hydrated lithium ion is four-coordinate in aqueous solution. New ionic radii are proposed for four- and six-coordinate lithium(I), 0.60 and 0.79 ?, respectively, as well as for five- and six-coordinate sodium(I), 1.02 and 1.07 ?, respectively. The ionic radii for six- and seven-coordinate K(+), 1.38 and 1.46 ?, respectively, and eight-coordinate Rb(+) and Cs(+), 1.64 and 1.73 ?, respectively, are confirmed from previous studies. The M-O bond distances in dimethyl sulfoxide solvated sodium, potassium, rubidium and cesium ions in solution are very similar to those observed in aqueous solution.     

A theoretical study of aqueous solvation of K comparing ab initio, polarizable, and fixed-charge models

The hydration of K(+) is studied using a hierarchy of theoretical approaches, including ab initio Born-Oppenheimer molecular dynamics and Car-Parrinello molecular dynamics, a polarizable force field model based on classical Drude oscillators, and a nonpolarizable fixed-charge potential based on the TIP3P water model. While models based more directly on quantum mechanics offer the possibility to account for complex electronic effects, polarizable and fixed-charges force fields allow for simulations of large systems and the calculation of thermodynamic observables with relatively modest computational costs. A particular emphasis is placed on investigating the sensitivity of the polarizable model to reproduce key aspects of aqueous K(+), such as the coordination structure, the bulk hydration free energy, and the self diffusion of K(+). It is generally found that, while the simple functional form of the polarizable Drude model imposes some restrictions on the range of properties that can simultaneously be fitted, the resulting hydration structure for aqueous K(+) agrees well with experiment and with more sophisticated computational models. A counterintuitive result, seen in Car-Parrinello molecular dynamics and in simulations with the Drude polarizable force field, is that the average induced molecular dipole of the water molecules within the first hydration shell around K(+) is slightly smaller than the corresponding value in the bulk. In final analysis, the perspective of K(+) hydration emerging from the various computational models is broadly consistent with experimental data, though at a finer level there remain a number of issues that should be resolved to further our ability in modeling ion hydration accurately.     

Structure and dynamics of Au+ ion in aqueous solution: ab initio QM/MM MD simulations

Structure and dynamics of hydrated Au(+) have been investigated by means of molecular dynamics simulations based on ab initio quantum mechanical molecular mechanical forces at Hartree-Fock level for the treatment of the first hydration shell. The outer region of the system was described using a newly constructed classical three-body corrected potential. The structure was evaluated in terms of radial and angular distribution functions and coordination number distributions. Water exchange processes between coordination shells and bulk indicate a very labile structure of the first hydration shell whose average coordination number of 4.7 is a mixture of 3-, 4-, 5-, 6-, and 7-coordinated species. Fast water exchange reactions between first and second hydration shell occur, and the second hydration shell is exceptionally large. Therefore, the mean residence time of water molecules in the first hydration shell (5.6 ps/7.5 ps for t*= 0.5 ps/2.0 ps) is shorter than that in the second shell (9.4 ps/21.2 ps for t*= 0.5 ps/2.0 ps), leading to a quite specific picture of a "structure-breaking" effect.     

<Emphasis Type="Italic">D</Emphasis>-Structure of Aqueous Solutions of Cobalt(II) Nitrate at 298 and 323 K by X-Ray Diffraction

Aqueous solutions of cobalt(II) nitrate with 1 : 15, 1 : 25, and 1 : 40 mole ratios at 298 and 323 K were studied by the X-ray diffraction. As the solution concentration decreases, ion triads (1 : 15) pass into contact ion pairs (1 : 25) and then to independently hydrated ions (1 : 40). The structural variations are accompanied by increase in a number of water molecules in the second coordination sphere of the cations and in the hydration shell of the anions. Heating produces destruction of ion triads in the 1 : 15 solution and ion association in the 1 : 40 solution. The structure of all the solutions at 323 K is characterized by a system of contact ion pairs.     

Ions in water: the microscopic structure of concentrated hydroxide solutions

Neutron-diffraction data on aqueous solutions of hydroxides, at solute concentrations ranging from 1 solute per 12 water molecules to 1 solute per 3 water molecules, are analyzed by means of a Monte Carlo simulation (empirical potential structure refinement), in order to determine the hydration shell of the OH- in the presence of the smaller alkali metal ions. It is demonstrated that the symmetry argument between H+ and OH- cannot be used, at least in the liquid phase at such high concentrations, for determining the hydroxide hydration shell. Water molecules in the hydration shell of K+ orient their dipole moment at about 45 degrees from the K+-water oxygen director, instead of radially as in the case of the Li+ and Na+ hydration shells. The K+-water oxygen radial distribution function shows a shallower first minimum compared to the other cation-water oxygen functions. The influence of the solutes on the water-water radial distribution functions is shown to have an effect on the water structure equivalent to an increase in the pressure of the water, depending on both ion concentration and ionic radius. The changes of the water structure in the presence of charged solutes and the differences among the hydration shells of the different cations are used to present a qualitative explanation of the observed cation mobility.     

Hydration structure of water confined between mica surfaces

We report further molecular dynamics simulations on the structure of bound hydration layers under extreme confinement between mica surfaces. We find that the liquid phase of water is maintained down to 2 monolayer (ML) thick, whereas the structure of the K(+) ion hydration shell is close to the bulk structure even under D = 0.92 nm confinement. Unexpectedly, the density of confined water remains approximately the bulk value or less, whereas the diffusion of water molecules decreases dramatically. Further increase in confinement leads to a transition to a bilayer ice, whose density is much less than that of ice Ih due to the formation of a specific hydrogen-bonding network.     

A theoretical study on anomalous temperature dependence of pKw of water

pH, with its well-known value of 7 at ambient condition, is a most basic property of water, with wide implications in chemistry and biology. The pH value is determined by the tendency of autoionization of water molecules into ion pairs, H(+) and OH(-), and is expected to vary extensively with the water condition, which determines the stability of the ion pairs. When temperature rises from the normal to the supercritical region, the pH of water experimentally exhibits complex, nonmonotonic temperature dependence, that is, it first decreases from 7 and then increases rapidly. Accurate theoretical evaluation of pH and microscopic understanding of this anomalous behavior have proven to be a challenging task because the hydration of these ions, especially for OH(-), is very difficult to reproduce. In the present study a molecular simulation is performed to understand this peculiar temperature dependence. The imbalance between the ion-water and the water-water molecular interaction strengths and the concomitant water density enhancement in the hydration shell, observed in the supercritical liquids, serve to put a subtle balance to produce this temperature dependence of the pH value. It is found that the large charge transfers from H(+) and OH(-) to the surrounding water molecules take place. In these transfers, not only water molecules in the neighboring hydration shell but also those in the outer hydration shell play a significant role. The coordination number of water molecules around OH(-) is found to be 4.5 at 300 K, which decreases slowly with temperature, for example, 4 at 800 K, in the present calculation.     

Formation and interaction of hydrated alkali metal ions at the graphite-water interface

Ion hydration at a solid surface ubiquitously exists in nature and plays important roles in many natural processes and technological applications. Aiming at obtaining a microscopic insight into the formation of such systems and interactions therein, we have investigated the hydration of alkali metal ions at a prototype surface-graphite (0001), using first-principles molecular dynamics simulations. At low water coverage, the alkali metal ions form two-dimensional hydration shells accommodating at most four (Li, Na) and three (K, Rb, Cs) waters in the first shell. These two-dimensional shells generally evolve into three-dimensional structures at higher water coverage, due to the competition between hydration and ion-surface interactions. Exceptionally K was found to reside at the graphite-water interface for water coverages up to bulk water limit, where it forms an "umbrellalike" surface hydration shell with an average water-ion-surface angle of 115 degrees . Interactions between the hydrated K and Na ions at the interface have also been studied. Water molecules seem to mediate an effective ion-ion interaction, which favors the aggregation of Na ions but prevents nucleation of K. These results agree with experimental observations in electron energy loss spectroscopy, desorption spectroscopy, and work function measurement. In addition, the sensitive dependence of charge transfer on dynamical structure evolution during the hydration process, implies the necessity to describe surface ion hydration from electronic structure calculations.     

Equatorial and apical solvent shells of the UO2 2+ ion

First principles molecular dynamics simulations of the hydration shells surrounding UO(2)(2+) ions are reported for temperatures near 300 K. Most of the simulations were done with 64 solvating water molecules (22 ps). Simulations with 122 water molecules (9 ps) were also carried out. The hydration structure predicted from the simulations was found to agree with very well-known results from x-ray data. The average U=O bond length was found to be 1.77 A. The first hydration shell contained five trigonally coordinated water molecules that were equatorially oriented about the O-U-O axis with the hydrogen atoms oriented away from the uranium atom. The five waters in the first shell were located at an average distance of 2.44 A (2.46 A, 122 water simulation). The second hydration shell was composed of distinct equatorial and apical regions resulting in a peak in the U-O radial distribution function at 4.59 A. The equatorial second shell contained ten water molecules hydrogen bonded to the five first shell molecules. Above and below the UO(2)(2+) ion, the water molecules were found to be significantly less structured. In these apical regions, water molecules were found to sporadically hydrogen bond to the oxygen atoms of the UO(2)(2+), oriented in such a way as to have their protons pointed toward the cation. While the number of apical waters varied greatly, an average of five to six waters was found in this region. Many water transfers into and out of the equatorial and apical second solvation shells were observed to occur on a picosecond time scale via dissociative mechanisms. Beyond these shells, the bonding pattern substantially returned to the tetrahedral structure of bulk water.     

Dynamical properties of the water molecules in the hydration shells of Fe(II) and Fe(III) ions: ab initio QM/MM molecular dynamics simulations

Dynamical properties, librational and vibrational motions of water molecules in the first and second hydration shells of the Fe(II) and Fe(III) ion were evaluated by means of velocity autocorrelation functions obtained by combined quantum mechanical/molecular mechanical molecular dynamics (QM/MM-MD) simulations. The frequencies of rotation around three principal axes and the frequencies of intramolecular vibration of the water molecules in the first hydration shells obtained from the simulations are blue-shifted for both ions compared to those observed experimentally for liquid water. The intramolecular geometry of water molecules in the quantum mechanically treated region (ion plus first hydration shell) shows shorter O–H bonds and wider H–O–H angles than the bulk solvent.     

Long-range hydrogen-bond structure in aqueous solutions and the vapor-water interface

There is a considerable disagreement about the extent to which solutes perturb water structure. On the one hand, studies that analyse structure directly only show local structuring in a solute's first and possibly second hydration shells. On the other hand, thermodynamic and kinetic data imply indirectly that structuring occurs much further away. Here, the hydrogen-bond structure of water around halide anions, alkali cations, noble-gas solutes, and at the vapor-water interface is examined using molecular dynamics simulations. In addition to the expected perturbation in the first hydration shell, deviations from bulk behavior are observed at longer range in the rest of the simulation box. In particular, at the longer range, there is an excess of acceptors around halide anions, an excess of donors around alkali cations, weakly enhanced tetrahedrality and an oscillating excess and deficiency of donors and acceptors around noble-gas solutes, and enhanced tetrahedrality at the vapor-water interface. The structuring compensates for the short-range perturbation in water-water hydrogen bonds induced by the solute. Rather than being confined close to the solute, it is spread over as many water molecules as possible, presumably to minimize the perturbation to each water molecule.