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.     

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.     

Structure and electric properties of sodium ion hydrate shell in nanopore with hydrophilic walls

The method of molecular–level computer simulation at the temperature of 298 K was used to study the fundamental regularities of formation of electric properties of the hydrate shell of the Na⁺ cation in a planar model nanopore with hydrophilic structureless walls in contact with water vapors. Electric polarizability changes nonmonotonously: as consistent with the changes in the molecular structure of the system. Hydration within the pore occurs in several stages, from formation of chain structures, microdrop compaction and ejection of the ion from its own hydrate shell to encapsulation and absorption of the ion by the solvent preceding formation of nanoelectrolyte. Despite the significant differences in the energy of retaining hydrate shells for Na⁺ and Cl^─ ions, polarizabilities of the two systems are close and behave similarly under variation of conditions. Strong spatial anisotropy of the polarizability tensor of the ion–hydrate complex is due to the effect of the nanopore walls on multiparticle spatial correlations in the system.     

Ion current rectification at nanopores in glass membranes

The origin of ion current rectification observed at conical-shaped nanopores in glass membranes immersed in KCl solutions has been investigated using finite-element simulations. The ion concentrations and fluxes (due to diffusion, migration, and electroosmotic convection) were determined by the simultaneous solution of the Nernst-Planck, Poisson, and Navier-Stokes equations for the two-ion (K+ and Cl-) system. Fixed surface charge on both the internal and external glass surfaces that define the pore structure was included to account for electric fields and nonuniform ion conductivity within the nanopores and electric fields in the external solution near the pore mouth. We demonstrate that previous observations of ion current rectification in conical-shaped glass nanopores are a consequence of the voltage-dependent solution conductivity in the vicinity of the pore mouth, both inside and outside of the pore. The simulations also demonstrate that current rectification is maximized at intermediate bulk ion concentrations, a combination of (i) the electrical screening of surface charge at high concentrations and (ii) a fixed number of charge-carrying ions in the pore at lower concentration, which are physical conditions where the voltage dependence of the conductivity disappears. In addition, we have quantitatively shown that electroosmotic flow gives rise to a significant but small contribution to current rectification.     

Modeling growth of organized nanoporous structures by anodic oxidation

Nanostructured porous oxides are produced by anodic dissolution of several metals. A scaling approach is introduced to explain pattern nucleation in an oxide layer, and a related microscopic model shows oxide growth with long nanopores. The scaling approach matches the time of ion transport across the thin oxide layer, which is related to metal corrosion, and the time of diffusion along the oxide/solution (OS) interface, which represents the extension of oxide dissolution. The selected pattern size is of order (dD(S)/v(O))(1/2), where d is the oxide thickness, v(O) is the migration velocity of oxygen ions across the oxide, and D(s) is the diffusion coefficient of H(+) ions along the oxide/solution interface. This result is consistent with available experimental data for those quantities, predicts the increase of pore size with the external voltage, and suggests the independence of pore size with the solution pH. Subsequently, we propose a microscopic model that expresses the main physicochemical processes as a set of characteristic lengths for diffusion and surface relaxation. It shows a randomly perturbed OS interface at short times, its evolution to pore nucleation and to stable growth of very long pores, in agreement with the mechanistic scenario suggested by two experimental groups. The decrease of the size of the walls between the pores with the interface tension is consistent with arguments for formation of titania nanotube arrays instead of nanopores. These models show that pattern nucleation and growth depend on matching a small number of physicochemical parameters, which is probably the reason for the production of nanostructured porous oxides from various materials under suitable electrochemical conditions.     

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 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.     

Electric-field-controlled water and ion permeation of a hydrophobic nanopore

The permeation of hydrophobic, cylindrical nanopores by water molecules and ions is investigated under equilibrium and out-of-equilibrium conditions by extensive molecular-dynamics simulations. Neglecting the chemical structure of the confining pore surface, we focus on the effects of pore radius and electric field on permeation. The simulations confirm the intermittent filling of the pore by water, reported earlier under equilibrium conditions for pore radii larger than a critical radius R(c). Below this radius, water can still permeate the pore under the action of a strong electric field generated by an ion concentration imbalance at both ends of the pore embedded in a structureless membrane. The water driven into the channel undergoes considerable electrostriction characterized by a mean density up to twice the bulk density and by a dramatic drop in dielectric permittivity which can be traced back to a considerable distortion of the hydrogen-bond network inside the pore. The free-energy barrier to ion permeation is estimated by a variant of umbrella sampling for Na(+), K(+), Ca(2+), and Cl(-) ions, and correlates well with known solvation free energies in bulk water. Starting from an initial imbalance in ion concentration, equilibrium is gradually restored by successive ion passages through the water-filled pore. At each passage the electric field across the pore drops, reducing the initial electrostriction, until the pore, of radius less than R(c), closes to water and hence to ion transport, thus providing a possible mechanism for voltage-dependent gating of hydrophobic pores.     

Metal–Organic Framework Membrane Nanopores as Biomimetic Photoresponsive Ion Channels and Photodriven Ion Pumps

Biological ion channels and ion pumps with sub-nanometer sizes modulate ion transport in response to external stimuli. Realizing such functions with sub-nanometer solid-state nanopores has been an important topic with wide practical applications. Herein, we demonstrate a biomimetic photoresponsive ion channel and photodriven ion pump using a porphyrin-based metal–organic framework membrane with pore sizes comparable to hydrated ions. We show that the molecular-size pores enable precise and robust optoelectronic ion transport modulation in a broad range of concentrations, unparalleled with conventional solid-state nanopores. Upon decoration with platinum nanoparticles to form a Schottky barrier photodiode, photovoltage across the membrane is generated with “uphill” ion transport from low concentration to high concentration. These results may spark applications in energy conversion, ion sieving, and artificial photosynthesis.     

Modeling the selective partitioning of cations into negatively charged nanopores in water

Partitioning and transport of water and small solutes into and through nanopores are important to a variety of chemical and biological processes and applications. Here we study water structure in negatively charged model cylindrical [carbon nanotube (CNT)-like] nanopores, as well as the partitioning of positive ions of increasing size (Na+, K+, and Cs+) into the pore interior using extensive molecular dynamics simulations. Despite the simplicity of the simulation system-containing a short CNT-like nanopore in water carrying a uniformly distributed charge of qpore=-ne surrounded by n (=0,...,8) cations, making the overall system charge neutral-the results provide new and useful insights on both the pore hydration and ion partitioning. For n=0, that is, for a neutral nanopore, water molecules partition into the pore and form single-file hydrogen-bonded wire spanning the pore length. With increasing n, water molecules enter the pore from both ends with preferred orientations, resulting in a mutual repulsion between oriented water molecules at the pore center and creating a cavity-like low density region at the center. For low negative charge densities on the pore, the driving force for partitioning of positive ions into the pore is weak, and no partitioning is observed. Increasing the pore charge gradually leads to partitioning of positive ions into the pore. Interestingly, over a range of intermediate negative charge densities, nanopores display both thermodynamic as well as kinetic selectivity toward partitioning of the larger K+ and Cs+ ions into their interior over the smaller Na+ ions. Specifically, the driving force is in the order K+>Cs+>Na+, and K+ and Cs+ ions enter the pore much more rapidly than Na+ ions. At higher charge densities, the driving force for partitioning increases for all cations-it is highest for K+ ions-and becomes similar for Na+ and Cs+ ions. The variation of thermodynamic driving force and the average partitioning time with the pore charge density together suggest the presence of free energy barriers in the partitioning process. We discuss the role of ion hydration in the bulk and in the pore interior as well as of the pore hydration in determining the barrier heights for ion partitioning and the observed thermodynamic and kinetic selectivities.     

Metal–Organic Framework Membrane Nanopores as Biomimetic Photoresponsive Ion Channels and Photodriven Ion Pumps

Biological ion channels and ion pumps with sub‐nanometer sizes modulate ion transport in response to external stimuli. Realizing such functions with sub‐nanometer solid‐state nanopores has been an important topic with wide practical applications. Herein, we demonstrate a biomimetic photoresponsive ion channel and photodriven ion pump using a porphyrin‐based metal–organic framework membrane with pore sizes comparable to hydrated ions. We show that the molecular‐size pores enable precise and robust optoelectronic ion transport modulation in a broad range of concentrations, unparalleled with conventional solid‐state nanopores. Upon decoration with platinum nanoparticles to form a Schottky barrier photodiode, photovoltage across the membrane is generated with “uphill” ion transport from low concentration to high concentration. These results may spark applications in energy conversion, ion sieving, and artificial photosynthesis.     

Transport properties and distribution of water molecules confined in hydrophobic nanopores and nanoslits

The transport properties, including the diffusivity and viscosity, of water confined in hydrophobic nanopores and nanoslits were studied by molecular dynamics simulations. The results show that the diffusion coefficient in nanopores and nanoslits is markedly lower than that in the bulk. But the viscosity is much larger than that in bulk. The parallel diffusion coefficient is obviously larger than the perpendicular ones. The diffusion coefficient in the channel pore is ever less than that in the slit pore at the same pore width, but the viscosity is larger. The temperature and density affect significantly the diffusivity and viscosity in nanopores and nanoslits. Lower density water exhibits some special characteristics on density profiles in nanopores and nanoslits at lower temperatures, and the density profiles show a change from homogeneous to inhomogeneous as the pore width is reduced. Even clusters occurred in micropores.     

Synergistic co-entrapment and triggered release in hollow nanocapsules with uniform nanopores

We describe a new co-entrapment and release motif based on the combination of noncovalent and steric interactions in materials with well-defined nanopores. Individual components enter hollow nanocapsules through nanopores in the capsule shell. Their complex, larger than the pore size, remains entrapped. The dissociation of the complex upon external stimulus releases entrapped components. Reversible formation of complexes between diaza-18-crown-6 and metal ions was used to demonstrate the feasibility of new approach to co-entrapment and triggered release.     

Rotaxane‐Like Structures Threaded through the Pores of Hollow Porous Nanocapusles

Nanocapsules with molecules threaded through the porous shells may lead to advanced cell‐mimicking functional devices. Herein, we show the feasibility of synthesizing such hybrid nanostructures by using vesicle‐templated polymer nanocapsules with controlled nanopores. Ship‐in‐a‐bottle assembly inside a nanocapsule created an internal unit. An external unit was then connected to an entrapped internal unit through pre‐attached linker threaded through a nanopore in the shell of the nanocapsule. Both internal and external units are larger than the pore size and cannot cross the shell, producing a rotaxane‐like structure. Successful synthesis was achieved with fairly short linkers (six and ten carbon atoms in a chain), creating an opportunity for facile synthesis of functional devices capable of cross‐shell communication.     

Molecular simulation of nanoclusters of gas hydrates in a water shell. The mechanical state of the system

The molecular dynamics method is employed to study hydrates of methane (sI), and krypton hydrate (sII), as well as an ice nanocluster in a supercooled water shell. The main attention is focused on the local structure and the mechanical state of two-phase nanosized systems, which is described using the local pressure tensor. Analysis of the temperature dependence of the local pressure allows one to compare two possible mechanisms responsible for the anomalous stability of gas hydrates at ambient pressure. According to the first mechanism, the water shell plays the role of a barrier that prevents the gas from escaping from the hydrate core. The second mechanism implies that the water shell generates additional pressure, which transfers the hydrate to a thermodynamically stable state. Results of molecular dynamics simulation indicate that both mechanisms are simultaneously involved in the stabilization of the hydrate nanocluster.     

模板表面对间规聚苯乙烯在纳米模板中结晶取向的影响

以偏振显微红外光谱方法研究间规聚苯乙烯（sPS）在阳极氧化铝（AAO）模板孔洞内的结晶取向行为。 以正己基三甲氧基硅烷修饰AAO模板孔洞表面,使其烷基化,探索表面性质对不同尺寸孔洞内sPS结晶取向的影响。 结果表明,sPS在255 ℃温度下结晶,而且随孔洞尺寸的减小,纳米孔洞内sPS分子链的垂直取向程度均降低,并且相同孔径尺寸下在表面烷基化的孔洞内sPS晶区分子链的垂直取向程度更低。 这些现象可归因于分子链与孔壁间相互作用的不同导致孔壁表面对晶核取向的诱导。     

Quasi one-dimensional nanopores in single-wall carbon nanohorn colloids using grand canonical Monte Carlo simulation aided adsorption technique

The average interstitial nanopore structure of single-wall carbon nanohorn (SWNH) assemblies was determined using X-ray diffraction and grand canonical Monte Carlo (GCMC) simulation aided N(2) adsorption at 77 K. The interstitial nanopores of SWNH assemblies can be regarded as quasi one-dimensional pores due to the partial orientation of the SWNH particles; the average pore width of the interstitial pores is 0.6 nm. Good agreement between the GCMC simulation of a structural model with one-dimensional interstitial nanopores and an experimental adsorption isotherm below P/P(0) = 10(-4) is evidence of the quasi one-dimensionality of the interstitial nanopores. A snapshot from the GCMC simulation showed one-dimensional growth of adsorbed N(2) molecules.     

Fabrication and functionalization of nanochannels by electron-beam-induced silicon oxide deposition

We report on the fabrication and electrical characterization of functionalized solid-state nanopores in low stress silicon nitride membranes. First, a pore of approximately 50 nm diameter was drilled using a focused ion beam technique, followed by the local deposition of silicon dioxide. A low-energy electron beam induced the decomposition of adsorbed tetraethyl orthosilicate resulting in site-selective functionalization of the nanopore by the formation of highly insulating silicon oxide. The deposition occurs monolayer by monolayer, which allows for control of the final diameter with subnanometer accuracy. Changes in the pore diameter could be monitored in real time by scanning electron microscopy. Recorded ion currents flowing through a single nanopore revealed asymmetry in the ion conduction properties with the sign of the applied potential. The low-frequency excess noise observed at negative voltage originated from stepwise conductance fluctuations of the open pore.     

Ionic exclusion phase transition in neutral and weakly charged cylindrical nanopores

A field theoretic variational approach is introduced to study ion penetration into water-filled cylindrical nanopores in equilibrium with a bulk reservoir [S. Buyukdagli, M. Manghi, and J. Palmeri, Phys. Rev. Lett. 105, 158103 (2010)]. It is shown that an ion located in a neutral pore undergoes two opposing mechanisms: (i) a deformation of its surrounding ionic cloud of opposite charge, with respect to the reservoir, which increases the surface tension and tends to exclude ions from the pore, and (ii) an attractive contribution to the ion self-energy due to the increased screening with ion penetration of the repulsive image forces associated with the dielectric jump between the solvent and the pore wall. For pore radii around 1 nm and bulk concentrations lower than 0.2 mol/l, this mechanism leads to a first-order phase transition, similar to capillary "evaporation," from an ionic-penetration state to an ionic-exclusion state. The discontinuous phase transition exists within the biological concentration range (～0.15 mol/l) for small enough membrane dielectric constants (ε(m) < 5). In the case of a weakly charged pore, counterion penetration exhibits a nonmonotonic behavior and is characterized by two regimes: at low reservoir concentrations or small pore radii, coions are excluded and counterions enter the pore to enforce electroneutrality; dielectric repulsion (image forces) remain strong and the counterion partition coefficient decreases with increasing reservoir concentration up to a characteristic value. For larger reservoir concentrations, image forces are screened and the partition coefficient of counterions increases with the reservoir concentration, as in the neutral pore case. Large surface charge densities (>2 × 10(-3) e/nm(2)) suppress the discontinuous transition by reducing the energy barrier for ion penetration and shifting the critical point toward very small pore sizes and reservoir concentrations. Our variational method is also compared to a previous self-consistent approach and yields important quantitative corrections. The role of the curvature of dielectric interfaces is highlighted by comparing ionic penetration into slit and cylindrical pores. Finally, a charge regulation model is introduced in order to explain the key effect of pH on ionic exclusion and explain the origin of observed time-dependent nanopore electric conductivity fluctuations and their correlation with those of the pore surface charge.