Water vapor clustering in the field of Na<Superscript>+</Superscript> cation inside a nanopore with hydrophilic walls. 1. Spatial organization

Computer simulation has been employed to study the structure of a hydration shell of a Na⁺ ion under the conditions of a planar nanopore with structureless hydrophilic walls at 298 K. Intermolecular interactions have been described in terms of a detailed model calibrated with respect to experimental data on the free energy and enthalpy of the initial reactions of vapor molecule attachment to the ion. In the field of hydrophilic walls, the hydration shell is disrupted into an enveloping part and that spread over the surface of the walls. At the final stage of hydration, states with asymmetric distribution of molecules on opposite walls survive and the phenomenon of ion displacement out of its shell is stably reproduced. The orientational molecular order in the system strongly depends on the degree of wall hydrophilicity. The hydration shell of a sodium ion is less stable with respect to disturbances generated by the field of hydrophilic walls than the shell of a chlorine ion is.     

Hydration of Cl<Superscript>–</Superscript> ion in a planar nanopore with hydrophilic walls. 2. Thermodynamic stability

The Monte Carlo bicanonical statistical ensemble method has been employed to calculate the dependences of the Gibbs free energy, formation work, and entropy on the size of a hydration shell grown from water vapor on single-charged chlorine anion in a model planar nanopore with hydrophilic structureless walls at 298 K. A refined model comprising many-particle polarization interactions and calibrated with respect to experimental data on the free energy and enthalpy of the initial reactions of attachment of water molecules to the ion has been used. It has been found that a weak hydrophilicity of pore walls leads to destabilization of the hydration shell, while a strong one, on the contrary, causes its stabilization. The physical reason for the instability in the field of hydrophilic walls qualitatively differs from that under the conditions of hydration in bulk water vapor.     

Water vapor clustering in the field of a chlorine anion occurring in a planar nanopore with structureless walls

The Monte Carlo bicanonical statistical ensemble method has been employed to calculate the free energy, entropy, and work of Cl^? ion hydration in model planar pores 0.5 and 0.7 nm wide at 298 and 400 K. A detailed model of many-body interactions with the ion has been used, the model being matched to experimental data with respect to the free energy and enthalpy of attachment reaction in water vapor. Under the conditions of a restricted volume, the equilibrium size of a hydration shell substantially decreases, with the effect becoming stronger in the range of moderate and large sizes. In moderately supersaturated vapors, under the conditions of a nanopore, the ion loses its hydration shell as the temperature is decreased. In supersaturated vapors, the hydration shell formed on the ion is thermodynamically stable, while the stability crisis shifts to the region of larger sizes. The enhancement of the thermodynamic stability in the pore results from a rise in the chemical potential of molecules due to the deficiency of closet neighbors and a reduction in the entropy under the conditions of the restricted volume. As the temperature is elevated, the effect of ion displacement out of its hydration shell is leveled. The regularities derived in terms of the estimation model based on the capillary approximation are in qualitative agreement with the results of computer simulation.     

Water vapor nucleation on ion pairs under the conditions of a planar nanopore

Computer simulation has been employed to study the effect of a confined space of a planar model pore with structureless hydrophobic walls on the hydration of Na⁺Cl^– ion pairs in water vapor at room temperature. A detailed many-body model of intermolecular interactions has been used. The model has been calibrated relative to experimental data on the free energy and enthalpy of the initial reactions of water molecule attachment to ions and the results of quantum-chemical calculations of the geometry and energy of Na⁺Cl^– (H₂O)_N clusters in stable configurations, as well as spectroscopic data on Na⁺Cl^– dimer vibration frequencies. The free energy and work of hydration, as well as the adsorption curve, have been calculated from the first principles by the bicanonical statistical ensemble method. The dependence of hydration shell size on interionic distance has been calculated by the method of compensation potential. The transition between the states of a contact (CIP) and a solvent-separated ion pair (SSIP) has been reproduced under the conditions of a nanopore. The influence of the pore increases with the hydration shell size and leads to the stabilization of the SSIP states, which are only conditionally stable in bulk water vapor.     

Thermodynamic characteristics of the hydrate shell of a Na+ ion in a plane nanopore with hydrophobic walls

The chemical potential, free energy, and work of hydration of a single-charged sodium cation are calculated using the Monte Carlo method for a bicanonic statistic ensemble at the molecular level at 298 K in plane model nanopores 0.5 and 0.7 nm wide. It is shown that the nanopores have a stabilizing effect on the hydrate shell of an ion. It is concluded that the crisis of stability that occurs outside a pore is transformed into an abrupt acceleration of growth with the conservation of a stable equilibrium with vapor under the conditions of plane nanopores. It is established that the mechanism of the threshold acceleration of growth inside a pore is associated with an ion being displaced from its own hydrate shell.     

Hydration of Cl<Superscript>–</Superscript> ion in a planar nanopore with hydrophilic walls. 1. Molecular structure

Computer simulation has been employed to obtain equilibrium molecular configurations, as well as spatial and angular distributions of water molecules, under the action of the field of a single-charged chlorine anion in a model planar nanopore with structureless walls at room temperature. A detailed many-body model of intermolecular interactions calibrated in accordance with experimental data relative to the free energy of hydration in water vapor has been used. The effect of the hydrophilicity of the walls on the ion hydration shell consists in its disintegration into two parts, i.e., molecules retained exclusively due to the interactions with the ion and those adsorbed on the walls. In the regime of strong interactions with the walls, two relatively stable states arise with asymmetric distribution of molecules between opposite walls. The existence of the two metastable states destabilizes the position of ions inside a pore and is expected to accelerate their adsorption on the walls.     

Charge separation in Na<Superscript>+</Superscript>Cl<Superscript>-</Superscript>(H<Subscript>2</Subscript>O)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters in water vapors. 1. Intermolecular interactions

Charge separation in “soft” nanoparticles composed of water molecules, as well as sodium and chlorine ions, is studied by computer simulation. The detailed model of intermolecular interactions that includes, in addition to Coulomb, exchange, and dispersion forces, many-particle polarization and covalent interactions, as well as the effect due to the transfer of excess ion charges and influence of ion field on molecular interactions, is constructed. Model potentials are calibrated using experimental data on the free energy and enthalpy of the addition of vapor molecules to the hydration shells of ions, as well as the data of quantum-chemical calculations for stable cluster configurations and the vibration frequency of interionic bonds. The allowance for many-particle interactions makes it possible to improve the agreement between experimental and quantum-chemical data by more than an order of magnitude. The disregard for many-particle interactions leads to the significant overestimation of cluster stability.     

Structure of a Na<Superscript>+</Superscript> cation hydration shell on heating in a planar nanopore

Resistance to heating above the boiling point of water of the molecular structure of a single-charged sodium cation hydration shell growing under the conditions of a model planar nanopore with a width of 5 Å is studied by computer simulation. Monte Carlo calculations of spatial correlation functions are performed in a detailed model with regard to many-body interactions between the ion and water molecules. The system demonstrates an increased resistance to thermal fluctuations along the pore plane and a decreased one in the transverse direction. The heating is accompanied by an enhanced coating effect of molecules around the ion and a diminished effect of extruding the ion out of its own hydration shell. The orientational molecular order due to strong spatial anisotropy inside the nanopore is much more stable than the hydrogen bonds between the molecules.     

Charge separation in Na<Superscript>+</Superscript>Cl<Superscript>-</Superscript>(H<Subscript>2</Subscript>O)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters in water vapors. 2. Free energy

Charge separation in “soft” nanoparticles composed of water molecules, as well as sodium and chlorine ions, is studied by computer simulation. The detailed model of intermolecular interactions that includes, in addition to Coulomb, exchange, and dispersion forces, many-particle polarization and covalent interactions, as well as the effect due to the transfer of excess ion charges and influence of ion field on molecular interactions, is constructed. Model potentials are calibrated using experimental data on the free energy and enthalpy of the addition of vapor molecules to the hydration shells of ions, as well as the data of quantum-chemical calculations for stable cluster configurations and the vibration frequency of interionic bonds. The allowance for many-particle interactions makes it possible to improve the agreement between experimental and quantum-chemical data by more than an order of magnitude. The disregard for many-particle interactions leads to the significant overestimation of cluster stability.     

Water in extremely narrow planar pores with crystalline walls. 2. Thermodynamics

The free energy, entropy, and work of water vapor adsorption in planar pores with widths of 0.62 and 1.25 nm located in a silver iodide crystal parallel to its basal face have been computed at the molecular level. In contrast to adsorption on a free surface, the adsorption in the pores proceeds in three stages, i.e., the formation of molecular films on the walls, coalescence of the films, and densification of the fluid in the pore volume. At the second stage, the equilibrium between the fluid in the pore and the vapor over the pore at temperatures corresponding to normal conditions is thermodynamically unstable and accompanied by the development of a free energy barrier and the existence of metastable states. As temperature is elevated, the instability is gradually evened out; however, its signs remain preserved even at the boiling temperature of water. Extremely narrow pores with widths smaller than 1 nm are always filled with water under conditions of even a rather dry natural atmosphere. The filling of pores several nanometers wide in strongly unsaturated water vapors overcomes the free-energy barrier; however, the fluid that has filled the pore remains stable with respect to evaporation in vapors with densities lower than the density of saturated vapor by several orders of magnitude. The existence of the free-energy barrier and metastable states in nanosized breaks in crystals creates conditions for hysteresis of adsorption-desorption cycles.     

Computer simulation of the hydration of a chloride anion in a nanopore with hydrophilic walls

The hydration of a single-charged chloride anion Cl^- in a model plane nanopore with structureless hydrophilic walls in water vapor at room temperature is simulated using the Monte Carlo method. It is established that the adsorption of a fraction of associate molecules Cl^-(H₂O)_N on the walls enhances its thermodynamic stability and simulates the hydration of the ion at low vapor pressures. It is shown that a second stability crisis forms on the curve of the hydration work function in the mode of weak wall hydrophilicity.     

Phenomenon of the ousting of a monatomic ion from its hydration shell in flat nanopores

The structure and stability of hydrate shells of singly charged sodium and chlorine ions are studied by computer simulations under the conditions of nanoscopic flat pores with the use of the previously proposed detailed force field model containing polarization interactions, transferring charge effects as well as manybody interactions of covalent type. It is found that the effect of ousting a monatomic ion from its hydration shell, which has previously been observed by independent authors in bulk vapor, is also reproduced persistently in nanoscopic pores. Whereas the ousting of the ion from its hydration shell in bulk vapor is accompanied by the loss of thermodynamic stability of the system and at sufficiently high vapor pressure causes avalanche-like condensation, under the conditions of a nanoscopic pore the thermodynamic stability is retained. The obtained data show that the ousting of the ion from its hydration shell is a universal phenomenon covering the majority, if not all, of monatomic and, possibly, some of molecular ions.     

Computer simulation of molecular complexes H<Subscript>3</Subscript>O<Superscript>+</Superscript>(H<Subscript>2</Subscript>O)<Subscript>n</Subscript> under conditions of thermal fluctuations: I. Interactions in the system

The simplest pair model of intermolecular interactions fails to reproduce known experimental free energy and entropy of hydration of H₃O⁺ ions in water vapor. A fit to experiment is attained only when covalent bonds and nonpair interactions, which are of particular importance at contact distances from the ion, are taken into account. An interaction model was constructed, which allows the experimental free energies of cluster formation to be reproduced to fractions of k _B T by the Monte-Carlo method. Numerical values of interaction parameters were obtained by fitting simulated results to refined experimental data.Translated from Zhurnal Obshchei Khimii, Vol. 74, No. 9, 2004, pp. 1409–1417.Original Russian Text Copyright © 2004 by Shevkunov.This revised version was published online in April 2005 with a corrected cover date.     

Effect of hydrophilic walls on the hydration of sodium cations in planar nanopores

A computer simulation of the structure of Na⁺ ion hydration shells with sizes in the range of 1 to 100 molecules in a planar model nanopore 0.7 nm wide with structureless hydrophilic walls is performed using the Monte Carlo method at a temperature of 298 K. A detailed model of many-body intermolecular interactions, calibrated with reference to experimental data on the free energy and enthalpy of reactions after gaseous water molecules are added to a hydration shell, is used. It is found that perturbations produced by hydrophilic walls cause the hydration shell to decay into two components that differ in their spatial arrangement and molecular orientational order.     

Structure of the hydration shell of the Na+ ion in a planar nanopore with hydrophobic walls

The effect of steric hindrances in extremely narrow planar pores on the structure of the hydration shell of the single-charged sodium cation in water vapors at room temperature was studied by computer simulation. The deficiency of empty space for the motion in the slit-like pore was shown to slightly affect the radial distribution of molecules around the ion. The integrated (over the directions) numbers of ion-oxygen atom bonds of molecules in the ion’s hydration shell did not change despite the change in the shape of the hydration cluster from three- to two-dimensional. It was concluded that the changes in the positions of molecules relative to the ion were mainly reduced to azimuthal displacements; as a result, the local bulk density of molecules in the pore was higher than at the same distances outside the pore for the same total number of molecules. The distribution of molecules over layers inside the pore demonstrates the effect of molecules spread over the walls. The effect of ion displacement from its own hydration shell found earlier for the free chloride ion is steadily reproduced under the pore conditions. An alternative explanation to this effect was proposed that does not suggest high ion polarizability.     

Structure and electric properties of the hydration shell of a singly charged chloride ion in a nanopore with hydrophilic walls

The effect of hydrophilic walls on the structure of the hydration shell of a Cl^? ion is studied in terms of the model flat nanopore in contact with water vapors at room temperature by the Monte Carlo computerassisted simulations. In the field of hydrophilic walls, the hydration shell falls into two parts: the ion-enveloping part and the molecular-film spots spread over the wall surface above and under the ion. Both parts have the pronounced radial-layered structure. The three-dimensional scheme of distribution of the averaged local shell density represents a system of conical coaxial layers expanding in the direction from wall to ion. The effect of forcing out the ion from its own hydration shell is also observed for hydrophilic walls. The specific electric polarizability of the shell is strongly anisotropic. Its longitudinal component is several times larger than the transversal component and behaves nonmonotonically as the hydration shell grows, passing through the maximum. The molecular order near the walls is characterized by the preferential orientation of the molecule plane in parallel to the wall plane and the turn of symmetry axes of molecules in the direction parallel to the normal to the pore plane in the vicinity of the ion.     

Ion pairs in aqueous electrolyte microdrops under conditions of a flat nanopore

The molecular mechanisms of aqueous solvent penetration into a flat nanopore with hydrophobic structureless walls containing a Na⁺Cl^? ion pair with nonfixed distance between ions is studied by computer simulations. A detailed many-body polycenter model of intermolecular interactions calibrated with respect to experimental data for the free energy of attachment of water vapor molecules and quantum-chemical calculations in clusters is used. The ion pair hydration results in its decomposition. Drawing the molecules into the gap between ions makes easier penetration of solvent and filling of the nanopore with electrolyte. The ion-pair dissociation is accompanied by dramatic changes in the chemical potential of molecules and electric properties of the whole system. The thermodynamic characteristics of decomposition are stable as regards variations in the pore width. The post-decomposition electric polarizability demonstrates strong anisotropy associated with the nanopore flatness.     

Structure of the nearest surrounding of the Na<Superscript>+</Superscript> ion in aqueous solutions of its salts

Published data obtained by various research methods on structural characteristics of sodium ion hydration in aqueous solutions of its salts and authors, X-ray diffraction data have been generalized. Structural parameters of the nearest surrounding of Na⁺ ion, such as its coordination number, interparticle distances, and types of ion association, have been discussed. It has been noted that the coordination number of the cation changes from four to six upon dilution of the solutions.     

Mechanisms for ion retention in molecular water clusters in a planar nanopore against the background of thermal fluctuations

The Monte Carlo method has been used to calculate the potential of mean force for Na⁺ and Cl^? ions interacting in model planar nanopores with structureless walls under the conditions of the material contact with water vapor at room temperature and above water boiling point. The interactions have been described using a detailed many-body model calibrated with respect to experimental data on the free energy of attachment reactions and the results of quantum-chemical calculations. Dissociation becomes possible when the vapor density increases as a sufficient number of molecules are pulled into the field of the ions. The dissociation proceeds sooner under the conditions of the nanopore than in bulk water vapor. Hydration decreases the energy of the dissociated state; however, the entropy component of the free energy partly compensates for the decrease in the internal energy, thereby increasing the stability of a contact ion pair. After the dissociation of a contact ion pair (CIP), ions are retained within a cluster in the state of a solvent-separated ion pair (SSIP). Fluctuations in the number of pulled-in vapor molecules, which are correlated with fluctuations in the interionic distance, stabilize the SSIP states with respect to recombination, while a decrease in the screening of the field of ions under the conditions of the nanopore stabilize the SSIP states with respect to cluster decay. The conditions of the nanopore stimulate the passage of an ion pair from the CIP to the SSIP state due to the rearrangement of the statistical weights in favor of molecules being located in the interionic gap. Thus, under the conditions of the nanopore, the stability of the SSIP states increases with respect to both the recombination of the ions and the decay of the ion-molecular associate.     

Calculation of the hydration free energy difference between pyridine and its methyl-substituted derivatives by computer simulation methods

The difference of the hydration free energy of pyridine and its methyl- and symmetrically dimethyl-substituted derivatives has been calculated by the method of free energy perturbation. To check the precision of the results obtained, we have repeated the calculations using thermodynamic integration over different paths. Besides the hydration free energy, the difference in the energy and entropy of hydration between pyridine and monomethyl- and dimethylpyridines has also been determined. The obtained results clearly show that the hydration free energy of the pyridine derivatives becomes more negative with each additional methyl group. However, the accuracy of the calculation does not allow us to draw any conclusion about the dependence of the hydration free energy on the location of the methyl group. The analysis of the Coulomb and Lennard-Jones contributions to the hydration free energy differences has shown the dominance of the latter term. The comparison of the hydration energy and free energy values has shown that there is a strong compensation effect between the energetic and entropic terms of the free energy. The hydration energy of the solute becomes considerably more negative with each additional methyl group due to the dispersion attraction between the methyl group and the surrounding water molecules. The introduction of a methyl group results in an approximately 30 J/(mol K) decrease of the entropy of hydration, and hence, at 300 K, the entropic contribution to the hydration free energy increases by about 9 kJ/mol. Due to their opposite signs, the entropic and energetic contributions largely cancel each other, resulting in approximately an order of magnitude smaller value for the free energy.