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.     

“One dimensional” double layer. The effect of size asymmetry of cations and anions on charge-storage in ultranarrow nanopores—an Ising model theory

We develop a statistical mechanical theory of charge storage in quasi-single-file ionophilic nanopores with pure room temperature ionic liquid cations and anions of different size. The theory is mapped to an extension of the Ising model exploited earlier for the case of cations and anions of the same size. We calculate the differential capacitance and the stored energy density per unit surface area of the pore. Both show asymmetry in the dependence on electrode potential with respect to the potential of zero charge, related to the difference in the size of the ions, which will be interesting to investigate experimentally. It also approves the increase of charge storage capacity via obstructed charging, which in these systems emerges for charging nanopores with smaller ions.     

Salt-induced acceleration of chemical reactions in cellulose nanopores

Chemical reactions in charged nanopores, such as present in cellulose fibers, can be accelerated by adding an inert salt, that does not participate in the reaction. Due to a Donnan-like equilibrium between ions inside and outside the pores, the concentration of co-ions in the nanopores (having a charge of the same sign as that of the pore wall), is lower than the concentration in the bulk. The co-ion concentration in pores can be increased by adding an inert salt, which shifts the Donnan equilibrium. The increased concentration of reactants in pores results in faster reaction kinetics. Reactions of cellulose with periodate confirm these predictions.     

Asymmetrical nanopores in track membranes: Fabrication,the effect of nanopore shape and electric charge of pore walls,promising applications

The properties of asymmetrical nanopores prepared by chemical etching of tracks of accelerated heavy ions are studied. Procedures are developed for controlling the size and shape of pores within wide limits. The presence of charged functional groups on pore walls is an intrinsic property of track membranes, which makes them a convenient object for studying electrokinetic phenomena in nanocapillaries. In electrolyte solutions, the asymmetrical “track” membranes demonstrate the diode effect. Two methods for fabricating asymmetrical nanopores in polyethylene terephthalate films are proposed and introduced into practice. Specific features of both methods, their advantages and drawbacks are considered. In addition to the brief survey of available information on diode-like track membranes, the new results on the mechanism of pore formation and the peculiarities of their geometry and electrokinetic properties are discussed. The emerging and potential applications of track membranes with asymmetrical pores are discussed briefly.     

Enhanced anion electroadsorption into carbon molecular sieve electrodes in acidic media

We previously showed that, for neutral electrolytes of small cations and relatively larger anions, it is possible to design certain pore sizes in active carbons that are large enough to electroadsorb cations but too small to allow anion electroadsorption. This situation leads to an electrical double-layer (EDL) capacitance that is significant only at potentials that are negative to the potential of zero charge (PZC); hence, much smaller capacitance is measured at potentials positive to the PZC. It was found that when the electrolyte is a strong acid (e.g., H(2)SO(4), HCl), a considerable capacitance is observed at positive potentials, even when the average pore size is too small to allow the insertion of large anions in neutral electrolyte solutions. This effect disappears when the pore size becomes considerably larger than the size of the ions. In this case, the EDL capacitance at positive potentials for both neutral and acidic solutions is comparable. The following four-step mechanism was found to comply best with the experimental data: (1) By acid catalysis, the protons form carbonium species within the conjugated carbon network. (2) The anions react with the carbonium ions, providing uncharged species in an activated state, which are chemibound as surface groups to the walls of the pores. (3) Because these surface groups are effectively much smaller in size than are the charged ions, they can migrate by chemical bond exchange within the carbon skeleton via constrictions (known to exist in microporous and molecular sieving carbons), which are too narrow to accommodate hydrated charged species. (4) Upon reaching wider spaces, the uncharged species are reionized and solvated by water molecules, which can fill small pores. The justification for the above mechanism is thoroughly discussed and demonstrated by the experimental results.     

Interionic Interactions in Conducting Nanoconfinement

Interionic interactions in conducting nanopores determine how counterions may be packed in the pores subject to the applied voltage. In ideal metals, interactions are exponentially screened by metallic electrons. However, modern nanoporous electrodes are predominantly made of carbon materials. To what extent is this screening affected by a different mode of dielectric response in such materials? To answer this question we study Coulomb interaction of charges in cylindrical and slit pores that allow finite electric field penetration into the pore walls, as well as the Coulomb interaction in a nanogap between two thin walls of graphene modeled by a non‐local dielectric function. In all cases studied the screening was found to be subtly different than in metallic nanopores, but still strong enough to support realization of the so called superionic state in such pores.     

Carbon materials for supercapacitor application

The most commonly used electrode materials for electrochemical capacitors are activated carbons, because they are commercially available and cheap, and they can be produced with large specific surface area. However, only the electrochemically available surface area is useful for charging the electrical double layer (EDL). The EDL formation is especially efficient in carbon pores of size below 1 nm because of the lack of space charge and a good attraction of ions along the pore walls. The pore size should ideally match the size of the ions. However, for good dynamic charge propagation, some small mesopores are useful. An asymmetric configuration, where the positive and negative electrodes are constructed from different materials, e.g., activated carbon, transition metal oxide or conducting polymer, is of great interest because of an important extension of the operating voltage. In such a case, the energy as well as power is greatly increased. It appears that nanotubes are a perfect conducting additive and/or support for materials with pseudocapacitance properties, e.g. MnO(2), conducting polymers. Substitutional heteroatoms in the carbon network (nitrogen, oxygen) are a promising way to enhance the capacitance. Carbons obtained by one-step pyrolysis of organic precursors rich in heteroatoms (nitrogen and/or oxygen) are very interesting, because they are denser than activated carbons. The application of a novel type of electrolyte with a broad voltage window (ionic liquids) is considered, but the stability of this new generation of electrolyte during long term cycling of capacitors is not yet confirmed.     

Saturation of subnanometer pores in an electric double-layer capacitor

Improvements in the energy density of electric double-layer capacitors (EDLCs) can in particular be gained by enhancing their capacitance. Recent findings suggest that the specific capacitance can be increased by matching the sizes of pores and desolvated ions. However, on such matching, we evidenced that charge storage saturation can occur in organic electrolyte before reaching the maximum voltage, e.g. 2.7 V, due to the insufficiently developed porosity. The experimental charge is larger than the calculated on account of the size of rigid cations, because of the intercalation-like behaviour and/or distortion of ions. The experimental and calculated values are less coincident for the higher sweep rates, which reveals that the optimal average pore size should depend on the current load, tending to shift to higher values in the normal usage conditions of supercapacitors.     

Hydrothermally shrunk alumina nanopores and their application to DNA sensing

Hydrothermal treatment of anodized alumina membranes has been known for years and is believed to seal the pores by transforming aluminium oxide into lower density hydroxides. We demonstrate that, at least for 60 nm diameter pores grown from anodization in oxalic acid at 40 V, the hydrothermal treatment significantly shrinks but does not fully seal the nanopores. The pores shrink to a neck of less than 10 nm in diameter and 2-4 microm in length, in which the diffusion coefficient of ions is five orders of magnitude smaller than in the bulk. Because of a high electrolyte resistance through hydrothermally treated shrunken nanopores, they can be used for electrical sensing applications, as demonstrated using the example of DNA sensing. Hybridization of target DNA with a complementary ssDNA covalently immobilized inside the nanopores causes an increase in impedance by more than 50% while a noncomplementary ssDNA has no measurable effect.     

Adsorption of simple fluid on silica surface and nanopore: effect of surface chemistry and pore shape

This paper reports a molecular simulation study on the adsorption of simple fluids (argon at 77 K) on hydroxylated silica surfaces and nanopores. The effect of surface chemistry is addressed by considering substrates with either partially or fully hydroxylated surfaces. We also investigate the effect of pore shape on adsorption and capillary condensation by comparing the results for cylindrical and hexagonal nanopores having equivalent sections (i.e., equal section areas). Due to the increase in the polarity of the surface with the density of OH groups, the adsorbed amounts for fully hydroxylated surfaces are found to be larger than those for partially hydroxylated surfaces. Both the adsorption isotherms for the cylindrical and hexagonal pores conform to the typical behavior observed in the experiments for adsorption/condensation in cylindrical nanopores MCM-41. Capillary condensation occurs through an irreversible discontinuous transition between the partially filled and the completely filled configurations, while evaporation occurs through the displacement at equilibrium of a hemispherical meniscus along the pore axis. Our data are also used to discuss the effect of surface chemistry and pore shape on the BET method. The BET surface for fully hydroxylated surfaces is much larger (by 10-20%) than the true geometrical surface. In contrast, the BET surface significantly underestimates the true surface when partially hydroxylated surfaces are considered. These results suggest that the surface chemistry and the choice of the system adsorbate/adsorbent is crucial in determining the surface area of solids using the BET method.     

Investigating the translocation of λ-DNA molecules through PDMS nanopores

We investigate the translocation of λ-DNA molecules through resistive-pulse polydimethylsiloxane (PDMS) nanopore sensors. Single molecules of λ-DNA were detected as a transient current increase due to the effect of DNA charge on ionic current through the pore. DNA translocation was found to deviate from a Poisson process when the interval between translocations was comparable to the duration of translocation events, suggesting that translocation was impeded during the presence of another translocating molecule in the nanopore. Characterization of translocation at different voltage biases revealed that a critical voltage was necessary to drive DNA molecules through the nanopore. Above this critical voltage, frequency of translocation events was directly proportional to DNA concentration and voltage bias, suggesting that transport of DNA from the solution to the nanopore was the rate limiting step. These observations are consistent with experimental results on transport of DNA through nanopores and nanoslits and the theory of hydrodynamically driven polymer flow in pores.     

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.     

Monitoring structural changes of liquids frozen in nanopores

Less dense packing of molecules in frozen liquids confined to cylindrical glass pores was observed to depend on pore size. This conclusion was derived by monitoring the rotational tunneling of methyl protons, which reside on studied molecules, with nuclear magnetic resonance. For example, the tunneling frequency of dimethyl sulfide and propionic acid at 10 K was observed to be larger in pores than in bulk. This is interpreted as being due to a decrease in the hindering potential. In another type of tunneling spectrum which is due to methyl-methyl interaction, observed in acetyl acetone at 10 K, the splitting decreases as the pores become smaller. It is demonstrated that in both types of materials the shifts of the methyl tunneling splittings in pores are the result of the reduced intermolecular interaction in the pore core region. This in turn indicates that the unit cell size of liquids frozen in nanopores is slightly increased. The increase is largest in smallest pores.     

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.     

Atomic force microscopy imaging and electrical recording of lipid bilayers supported over microfabricated silicon chip nanopores: lab-on-a-chip system for lipid membranes and ion channels

We describe a silicon chip-based supported bilayer system to detect the presence of ion channels and their electrical conductance in lipid bilayers. Nanopores were produced in microfabricated silicon membranes by electron beam lithography as well as by using a finely focused ion beam. Thermal oxide was used to shrink pore sizes, if necessary, and to create an insulating surface. The chips with well-defined pores were easily mounted on a double-chamber plastic cell recording system, allowing for controlling the buffer conditions both above and below the window. The double-chamber system allowed using an atomic force microscopy (AFM) tip as one electrode and inserting a platinum wire as the second electrode under the membrane window, to measure electrical current across lipid bilayers that are suspended over the pores. Atomic force imaging, stiffness measurement, and electrical capacitance measurement show the feasibility of supporting lipid bilayers over defined nanopores: a key requirement to use any such technique for structure-function study of ion channels. Online addition of gramicidin, an ion-channel-forming peptide, resulted in electrical current flow across the bilayer, and the I-V curve that was measured using the conducting AFM tip indicates the presence of many conducting gramicidin ion channels.     

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.     

Assembling wormlike micelles in tubular nanopores by tuning surfactant-wall interactions

Threadlike molecular assemblies are excluded from narrow pores unless attractive interactions with the confining pore walls compensate for the loss of configurational entropy. Here we show that wormlike surfactant micelles can be assembled in the 8 nm tubular nanopores of SBA-15 silica by adjusting the surfactant-pore-wall interactions. The modulation of the interactions was achieved by coadsorption of a surface modifier that also provides control over the partitioning of wormlike aggregates between the bulk solution and the pore space. We anticipate that the concept of tuning the interactions with the pore wall will be applicable to a wide variety of self-assembling molecules and pores.     

Water adsorption in ion-bearing nanopores

Grand canonical Monte Carlo simulations are used to examine the adsorption of water into cylindrical nanopores containing single ions. The isotherms for water adsorbing into nanopores with radii of 0.44, 0.54, 0.64, and 0.74 nm and containing Na+, K+, Ca2+, Cl-, or F- at 298 K are computed. In all cases the nanopores are found to fill at reservoir chemical potentials below the chemical potential of saturated water vapor at 298 K. The threshold chemical potential is found to be sensitive to both the size of the channel and the ion species, with the anion-bearing pores filling at lower chemical potentials. Additionally, the filling threshold chemical potential is found to decrease as the radius of the pores is decreased. Pores with K+ and Cl- are compared, and the Cl- pores are found to exhibit higher water densities in the filled states and a more energetically favorable water structure while yielding lower per particle entropies. Sample simulation configurations are also examined and indicate that at low chemical potentials, the adsorbed water forms a cluster around the ion. Finally, the influence of the choice of water model on the adsorption isotherms is examined.